Optimal control of partial differential equations and nonlinear optimization

M. Hintermüller, M. Hinze, J. Sokołowski, S. Ulbrich, eds., Special issue to honour Guenter Leugering on his 65th birthday, 1 of Control & Cybernetics, Systems Research Institute, Polish Academy of Sciences, Warsaw, 2019, (Collection Published).

M. Hintermüller, J.F. Rodrigues, eds., Topics in Applied Analysis and Optimisation -- Partial Differential Equations, Stochastic and Numerical Analysis, CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, 396 pages, (Collection Published).

R. Henrion, Chapter 2: Calmness as a Constraint Qualification for M-Stationarity Conditions in MPECs, in: Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, D. Aussel, C.S. Lalitha, eds., Forum for Interdisciplinary Mathematics, Springer, Singapore, 2018, pp. 21--41, (Chapter Published), DOI 10.1007/978-981-10-4774-9 .

M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, Chapter 13: Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, 2017, pp. 305--353, (Chapter Published), DOI 10.1007/978-3-319-56602-3 .

M. Hintermüller, D. Wegner, Distributed and Boundary Control Problems for the Semidiscrete Cahn--Hilliard/Navier--Stokes System with Nonsmooth Ginzburg--Landau Energies, in: Topological Optimization and Optimal Transport in the Applied Sciences, M. Bergounioux, E. Oudet, M. Rumpf, G. Carlier, Th. Champion, F. Santambrogio, eds., 17 of Radon Series on Computational and Applied Mathematics, De Gruyter, Berlin, 2017, pp. 40--63, (Chapter Published).

P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, 22 of Springer INdAM Series, Springer International Publishing AG, Cham, 2017, xii+571 pages, (Collection Published).
Abstract
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

F.J. Aragón Artacho, R. Henrion, M.A. López-Cerdá, C. Sagastizábal, J.M. Borwein, eds., Special Issue: Advances in Monotone Operators Theory and Optimization, 25, issues 3 and 4, of Set-Valued and Variational Analysis, Springer International Publishing AG, Cham, 2017, 396 pages, (Collection Published).

D. Hömberg, G. Hu, eds., Issue on the workshop ``Electromagnetics -- Modelling, Simulation, Control and Industrial Applications'', 8, no. 3 of Discrete Contin. Dyn. Syst. Ser. S, American Institute of Mathematical Sciences, Springfield, 2015, 259 pages, (Collection Published).

P. Colli, G. Gilardi, D. Hömberg, E. Rocca, eds., Special Issue dedicated to Jürgen Sprekels on the Occasion of his 65th Birthday, 35, no. 6 of Discrete Contin. Dyn. Syst. Ser. A, American Institute of Mathematical Sciences, Springfield, 2015, 472 pages, (Collection Published).

P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON -- Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

A. Mielke, Chapter 21: Dissipative Quantum Mechanics Using GENERIC, in: Recent Trends in Dynamical Systems -- Proceedings of a Conference in Honor of Jürgen Scheurle, A. Johann, H.-P. Kruse, F. Rupp, S. Schmitz, eds., 35 of Springer Proceedings in Mathematics & Statistics, Springer, Basel et al., 2013, pp. 555--585, (Chapter Published).
Abstract
Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for Non-Equilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition. One of our models couples a quantum system to a finite number of heat baths each of which is described by a time-dependent temperature. The dissipation mechanism is modeled via the canonical correlation operator, which is the inverse of the Kubo-Mori metric for density matrices and which is strongly linked to the von Neumann entropy for quantum systems. Thus, one recovers the dissipative double-bracket operators of the Lindblad equations but encounters a correction term for the consistent coupling to the dissipative dynamics. For the finite-dimensional and isothermal case we provide a general existence result and discuss sufficient conditions that guarantee that all solutions converge to the unique thermal equilibrium state. Finally, we compare of our gradient flow formulation for quantum systems with the Wasserstein gradient flow formulation for the Fokker-Planck equation and the entropy gradient flow formulation for reversible Markov chains.

D. Hömberg, F. Tröltzsch, eds., System Modeling and Optimization, 25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 12--16, 2011, 391 of IFIP Advances in Information and Communication Technology, Springer, Heidelberg [et al.], 2013, 568 pages, (Collection Published).

K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Coupled Systems of Partial Differential Equations, 158 of Internat. Series Numer. Math., Birkhäuser, Basel et al., 2009, 345 pages, (Collection Published).

B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279--299, (Chapter Published).

R. Henrion, A. Kruger, J. Outrata, eds., Special Issue on: Variational Analysis and Generalised Differentiation, 16 of Set-Valued Analysis, Springer, Heidelberg, 2008, xii+231 pages, (Collection Published).

K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Control of Coupled Partial Differential Equations, 155 of Internat. Series Numer. Math., Birkhäuser, Berlin, 2007, 382 pages, (Collection Published).

P. Neittaanmäki, D. Tiba, J. Sprekels, Optimization of Elliptic Systems: Theory and Applications, Springer Monographs in Mathematics, Springer, New York, 2006, xvi+514 pages, (Monograph Published).

K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Complex Structures, 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, 289 pages, (Monograph Published).

M.H. Farshbaf Shaker, M. Gugat, H. Heitsch, R. Henrion, Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints, SIAM Journal on Control and Optimization, 58 (2020), pp. 2288--2311, DOI 10.1137/19M1269944 .
Abstract
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented.

M.J. Cánovas, M.J. Gisbert, R. Henrion, J. Parra, Lipschitz lower semicontinuity moduli for linear inequality systems, Journal of Mathematical Analysis and Applications, 2 (2020), pp. 124313/1--124313/21, DOI 10.1016/j.jmaa.2020.124313 .
Abstract
The paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, right-hand side and left-hand side perturbations. Inspired by [14], we introduce the Lipschitz lower semicontinuity-star as an intermediate notion between the Lipschitz lower semicontinuity and the well-known Aubin property. We provide explicit point-based formulae for the moduli (best constants) of all three Lipschitz properties in all three perturbation settings.

D. Kamzolov, P. Dvurechensky, A. Gasnikov, Universal intermediate gradient method for convex problems with inexact oracle, Optimization Methods & Software, published online on 17.01.2020, DOI 10.1080/10556788.2019.1711079 .

M.S. Aronna, J.F. Bonnans, A. Kröner, Optimal control of PDEs in a complex space setting: Application to the Schrödinger equation, SIAM Journal on Control and Optimization, 57 (2019), pp. 1390--1412, DOI 10.1137/17M1117653 .

L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, SIAM Journal on Applied Mathematics, 79 (2019), pp. 257--283, DOI 10.1137/18M1179183 .
Abstract
A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a Ge-on-Si microbridge are given. The highly favorable electronic properties of this design are demonstrated by steady-state simulations of the corresponding van Roosbroeck (drift-diffusion) system.

H. Antil, C.N. Rautenberg, Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications, SIAM Journal on Mathematical Analysis, 51 (2019), pp. 2479--2503, DOI 10.1137/18M1224970 .
Abstract
We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply. For special cases of the weights, the resulting variational problem is known to be equivalent to the fractional Poisson problem. The trace space for the weighted Sobolev space is identified to be embedded in a weighted L2 space. We propose a finite element scheme to solve the Euler-Lagrange equations, and for the image denoising application we propose an algorithm to identify the unknown weights. The approach is illustrated on several test problems and it yields better results when compared to the existing total variation techniques.

P. Colli, G. Gilardi, J. Sprekels, A distributed control problem for a fractional tumor growth model, Mathematics - Open Access Journal, 7 (2019), pp. 792/1--792/32, DOI 10.3390/math7090792 .
Abstract
In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a Cahn--Hilliard type phase field system modeling tumor growth that goes back to Hawkins-Daarud et al. (Int. J. Numer. Math. Biomed. Eng. 28 (2012), 3--24.) The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in the recent work Adv. Math. Sci. Appl. 28 (2019), 343--375 by the present authors. In our analysis, we show the Fréchet differentiability of the associated control-to-state operator, establish the existence of solutions to the associated adjoint system, and derive the first-order necessary conditions of optimality for a cost functional of tracking type.

P. Colli, G. Gilardi, J. Sprekels, Deep quench approximation and optimal control of general Cahn--Hilliard systems with fractional operators and double obstacle potentials, Discrete and Continuous Dynamical Systems -- Series S, published online on 21.12.2019, urlhttps://doi.org/10.3934/dcdss.2020213, DOI 10.3934/dcdss.2020213 .
Abstract
In the recent paper ”Well-posedness and regularity for a generalized fractional Cahn--Hilliard system”, the same authors derived general well-posedness and regularity results for a rather general system of evolutionary operator equations having the structure of a Cahn--Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn--Hilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper ”Optimal distributed control of a generalized fractional Cahn--Hilliard system” (Appl. Math. Optim. (2018), https://doi.org/10.1007/s00245-018-9540-7) by the same authors, an analysis of distributed optimal control problems was performed for such evolutionary systems, where only the differentiable case of certain polynomial and logarithmic double-well potentials could be admitted. Results concerning existence of optimizers and first-order necessary optimality conditions were derived, where more restrictive conditions on the operators A and B had to be assumed in order to be able to show differentiability properties for the associated control-to-state operator. In the present paper, we complement these results by studying a distributed control problem for such evolutionary systems in the case of nondifferentiable nonlinearities of double obstacle type. For such nonlinearities, it is well known that the standard constraint qualifications cannot be applied to construct appropriate Lagrange multipliers. To overcome this difficulty, we follow here the so-called ”deep quench” method. This technique, in which the nondifferentiable double obstacle nonlinearity is approximated by differentiable logarithmic nonlinearities, was first developed by P. Colli, M.H. Farshbaf-Shaker and J. Sprekels in the paper ”A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles” (Appl. Math. Optim. 71 (2015), pp. 1-24) and has proved to be a powerful tool in a number of optimal control problems with double obstacle potentials in the framework of systems of Cahn--Hilliard type. We first give a general convergence analysis of the deep quench approximation that includes an error estimate and then demonstrate that its use leads in the double obstacle case to appropriate first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint state system.

P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective Cahn--Hilliard system with double obstacles and dynamic boundary conditions: A `deep quench' approach, Journal of Convex Analysis, 26 (2019), pp. 485--514.
Abstract
In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents a difficulty for the analysis. In contrast to the previous paper Optimal velocity control of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions by the same authors, the bulk and surface free energies are of double obstacle type, which renders the state constraint nondifferentiable. It is well known that for such cases standard constraint qualifications are not satisfied so that standard methods do not apply to yield the existence of Lagrange multipliers. In this paper, we overcome this difficulty by taking advantage of results established in the quoted paper for logarithmic nonlinearities, using a so-called `deep quench approximation'. We derive results concerning the existence of optimal controls and the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system.

P. Colli, G. Gilardi, J. Sprekels, Recent results on well-posedness and optimal control for a class of generalized fractional Cahn--Hilliard systems, Control and Cybernetics, 48 (2019), pp. 153--197.

P. Colli, A. Signori, J. Sprekels, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 21.10.2019, urlhttps://doi.org/10.1007/s00245-019-09618-6, DOI 10.1007/s00245-019-09618-6 .
Abstract
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design the dispensation of some drugs to the patient. The cost functional is of tracking type, whereas the potential setting has been kept quite general in order to allow regular and singular potentials to be considered. In this direction, some relaxation terms have been introduced in the system. We show the well-posedness of the state system, the Fréchet differentiability of the control-to-state operator in a suitable functional analytic framework, and, lastly, we characterize the first-order necessary conditions of optimality in terms of a variational inequality involving the adjoint variables.

S.P. Frigeri, C.G. Gal, M. Grasselli, J. Sprekels, Strong solutions to nonlocal 2D Cahn--Hilliard--Navier--Stokes systems with nonconstant viscosity, degenerate mobility and singular potential, Nonlinearity, 32 (2019), pp. 678--727, DOI 10.1088/1361-6544/aaedd0 .
Abstract
We consider a nonlinear system which consists of the incompressible Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We suppose that the viscosity depends smoothly on the order parameter as well as the mobility. Moreover, we assume that the mobility is degenerate at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with no-slip boundary condition for the (average) velocity and homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the two-dimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weak-strong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal Cahn-Hilliard equation, with a given velocity field, in the three dimensional case as well.

G. Gilardi, J. Sprekels, Asymptotic limits and optimal control for the Cahn--Hilliard system with convection and dynamic boundary conditions, Nonlinear Analysis. An International Mathematical Journal, 178 (2019), pp. 1--31, DOI 10.1016/j.na.2018.07.007 .
Abstract
In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding chemical potential. While recent works addressed the case of viscous Cahn--Hilliard systems, the `pure' nonviscous case is investigated here. In its first part, the paper deals with the asymptotic behavior of the solutions as time approaches infinity. It is shown that the $omega$-limit of any trajectory can be characterized in terms of stationary solutions, provided the initial data are sufficiently smooth. The second part of the paper deals with the optimal control of the system by the fluid velocity. Results concerning existence and first-order necessary optimality conditions are proved. Here, we have to restrict ourselves to the case of everywhere defined smooth potentials. In both parts of the paper, we start from corresponding known results for the viscous case, derive sufficiently strong estimates that are uniform with respect to the (positive) viscosity parameter, and then let the viscosity tend to zero to establish the sought results for the nonviscous case.

P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Vietnam Journal of Mathematics, 47 (2019), pp. 793--812, DOI 10.1007/s10013-019-00355-5 .
Abstract
In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization.

J. Sprekels, H. Wu, Optimal distributed control of a Cahn--Hilliard--Darcy system with mass sources, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 24.01.2019, urlhttps://doi.org/10.1007/s00245-019-09555-4, DOI 10.1007/s00245-019-09555-4 .
Abstract
In this paper, we study an optimal control problem for a two-dimensional Cahn--Hilliard--Darcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the control-to-state operator is Fréchet differentiable between suitable Banach spaces and derive the first-order necessary optimality conditions in terms of the adjoint variables and the usual variational inequality.

M. Hintermüller, N. Strogies, Identification of the friction function in a semilinear system for gas transport through a network, Optimization Methods & Software, 35 (2020), pp. 576--617 (published online on 10.12.2019), DOI 10.1080/10556788.2019.1692206 .

D. Hömberg, K. Krumbiegel, N. Togobytska, Optimal control of multiphase steel production, Journal of Mathematics in Industry, 9 (2019), pp. 1--32, DOI 10.1186/s13362-019-0063-x .
Abstract
An optimal control problem for the production of multiphase steel is investigated, where the state equations are a semilinear heat equation and an ordinary differential equation, which describes the evolution of the ferrite phase fraction. The optimal control problem is analyzed and the first-order necessary and second-order sufficient optimality conditions are derived. For the numerical solution of the control problem reduced sequential quadratic programming (rSQP) method with a primal-dual active set strategy (PDAS) was applied. The numerical results were presented for the optimal control of a cooling line for production of hot rolled Mo-Mn dual phase steel.

R. Lasarzik, Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system, Numerical Functional Analysis and Optimization. An International Journal, 40 (2019), pp. 1721--1767, DOI 10.1080/01630563.2019.1632895 .
Abstract
We analyze the Ericksen--Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the earlier introduced measure-valued solutions. In this article, we argue that dissipative solutions can be numerically approximated by a relative simple scheme, which fulfills the norm-restriction on the director in every step. We introduce a semi-discrete scheme and derive an approximated version of the relative-energy inequality for solutions of this scheme. Passing to the limit in the semi-discretization, we attain dissipative solutions. Additionally, we introduce an optimal control scheme, show the existence of an optimal control and a possible approximation strategy. We prove that the cost functional is lower semi-continuous with respect to the convergence of this approximation and argue that an optimal control is attained in the case that there exists a solution admitting additional regularity.

M. Eigel, J. Neumann, R. Schneider, S. Wolf, Risk averse stochastic structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 334 (2018), pp. 470--482, DOI 10.1016/j.cma.2018.02.003 .
Abstract
A novel approach for risk-averse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common risk-aware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such high-dimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach.

L. Adam, M. Hintermüller, Th.M. Surowiec, A PDE-constrained optimization approach for topology optimization of strained photonic devices, Annali di Matematica Pura ed Applicata. Serie Quarta. Fondazione Annali di Matematica Pura ed Applicata, c/o Dipartimento di Matematica ``U. Dini'', Firenze; Springer-Verlag, Heidelberg. English, French, German, Italian, English abstracts., 19 (2018), pp. 521--557, DOI 10.1007/s11081-018-9394-5 .
Abstract
Recent studies have demonstrated the potential of using tensile-strained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multi-material phase-field approach to determine the optimal material configuration within a so-called Germanium-on-Silicon microbridge is considered. Here, an “optimal" configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the cross-section of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a non-linear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and second-order optimality conditions. For the numerical experiments, an array of first and second-order solution algorithms in function-space are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed.

L. Adam, M. Hintermüller, Th.M. Surowiec, A semismooth Newton method with analytical path-following for the $H^1$-projection onto the Gibbs simplex, IMA Journal of Numerical Analysis, 39 (2019), pp. 1276--1295 (published online on 07.06.2018), DOI 10.1093/imanum/dry034 .
Abstract
An efficient, function-space-based second-order method for the $H^1$-projection onto the Gibbs-simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau-Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.

H. Antil, C.N. Rautenberg, Fractional elliptic quasi-variational inequalities: Theory and numerics, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 20 (2018), pp. 1--24, DOI 10.4171/IFB/395 .

P. Colli, G. Gilardi, J. Sprekels, Optimal boundary control of a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition, Nonlinear Analysis. An International Mathematical Journal, 170 (2018), pp. 171--196, DOI 10.1016/j.na.2018.01.003 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing control literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter of the system, which models an additional nonconserving phase transition occurring on the surface of the domain. We show the Fr&aecute;chenett differentiability of the associated control-to-state operator in appropriate Banach spaces and derive results on the existence of optimal controls and on first-order necessary optimality conditions in terms of a variational inequality and the adjoint state system.

P. Colli, G. Gilardi, J. Sprekels, Optimal distributed control of a generalized fractional Cahn--Hilliard system, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 82 (2020), pp. 551--589 (published online on 15.11.2018), DOI 10.1007/s00245-018-9540-7 .
Abstract
In the recent paper “Well-posedness and regularity for a generalized fractional Cahn--Hilliard system” by the same authors, general well-posedness results have been established for a class of evolutionary systems of two equations having the structure of a viscous Cahn--Hilliard system, in which nonlinearities of double-well type occur. The operators appearing in the system equations are fractional versions in the spectral sense of general linear operators A,B, having compact resolvents, which are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. In this work we complement the results given in quoted paper by studying a distributed control problem for this evolutionary system. The main difficulty in the analysis is to establish a rigorous Fréchet differentiability result for the associated control-to-state mapping. This seems only to be possible if the state stays bounded, which, in turn, makes it necessary to postulate an additional global boundedness assumption. One typical situation, in which this assumption is satisfied, arises when B is the negative Laplacian with zero Dirichlet boundary conditions and the nonlinearity is smooth with polynomial growth of at most order four. Also a case with logarithmic nonlinearity can be handled. Under the global boundedness assumption, we establish existence and first-order necessary optimality conditions for the optimal control problem in terms of a variational inequality and the associated adjoint state system.

P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a viscous Cahn--Hilliard system with convection and dynamic boundary conditions, SIAM Journal on Control and Optimization, 56 (2018), pp. 1665--1691, DOI 10.1137/17M1146786 .
Abstract
In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn--Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents an additional difficulty for the analysis. The nonlinearities in the bulk and surface free energies are of logarithmic type, which entails that the thermodynamic forces driving the phase separation process may become singular. We show existence for the optimal control problem under investigation, prove the Fréchet differentiability of the associated control-to-state mapping in suitable Banach spaces, and derive the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system. Due to the strong nonlinear couplings between state variables and control, the corresponding proofs require a considerable analytical effort.

S. Frigeri, M. Grasselli, J. Sprekels, Optimal distributed control of two-dimensional nonlocal Cahn--Hilliard--Navier--Stokes systems with degenerate mobility and singular potential, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 81 (2020), pp. 889--931 (published online on 24.09.2018), DOI 10.1007/s00245-018-9524-7 .
Abstract
In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier-Stokes equations, nonlinearly coupled with a convective nonlocal Cahn-Hilliard equation. The system rules the evolution of the volume-averaged velocity of the mixture and the (relative) concentration difference of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a time-dependent external force acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the control-to-state map, and we establish first-order necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in [19]. There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in [14].

A. Hantoute, R. Henrion, P. Pérez-Aros, Subdifferential characterization of probability functions under Gaussian distribution, Mathematical Programming. A Publication of the Mathematical Programming Society, 174 (2019), pp. 167--194 (published online on 29.01.2018), DOI 10.1007/s10107-018-1237-9 .
Abstract
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates the consideration of subdifferentials for such typically just continuous functions. The aim of this paper is to provide subdifferential formulae of such functions in the case of Gaussian distributions for possibly infinite-dimensional decision variables and nonsmooth (locally Lipschitzian) input data. These formulae are based on the spheric-radial decomposition of Gaussian random vectors on the one hand and on a cone of directions of moderate growth on the other. By successively adding additional hypotheses, conditions are satisfied under which the probability function is locally Lipschitzian or even differentiable.

R. Henrion, W. Römisch, Problem-based optimal scenario generation and reduction in stochastic programming, Mathematical Programming. A Publication of the Mathematical Programming Society, pp. published online on 04.10.2018, urlhttps://doi.org/10.1007/s10107-018-1337-6, DOI 10.1007/s10107-018-1337-6 .
Abstract
Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear two-stage stochastic programs we show that the problem-based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi-infinite program. We show that the latter is convex if either right-hand sides or costs are random and can be transformed into a semi-infinite program in a number of cases. We also consider problem-based optimal scenario reduction for two-stage models and optimal scenario generation for chance constrained programs. Finally, we discuss problem-based scenario generation for the classical newsvendor problem.

M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn--Hilliard--Navier--Stokes system, Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences, 19 (2018), pp. 629--662, DOI 10.1007/s11081-018-9393-6 .
Abstract
This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn--Hilliard--Navier--Stokes system with variable densities. The free energy density associated to the Cahn--Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier--Stokes equation. A dual-weighed residual approach for goal-oriented adaptive finite elements is presented which is based on the concept of C-stationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given.

M. Hintermüller, C.N. Rautenberg, N. Strogies, Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 27 (2019), pp. 433--468 (published online on 14.07.2018), DOI 10.1007/s11228-018-0489-0 .
Abstract
Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.

M. Eigel, R. Müller, A posteriori error control for stationary coupled bulk-surface equations, IMA Journal of Numerical Analysis, 38 (2018), pp. 271--298 (published online on 09.03.2017), DOI 10.1093/imanum/drw080 .
Abstract
We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm with several benchmark examples.

M. Eigel, K. Sturm, Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation, Optimization Methods & Software, 33 (2018), pp. 268--296 (published online on 03.05.2017), DOI 10.1080/10556788.2017.1314471 .
Abstract
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments.

L. Adam, R. Henrion, J. Outrata, On M-stationarity conditions in MPECs and the associated qualification conditions, Mathematical Programming. A Publication of the Mathematical Programming Society, 168 (2018), pp. 229--259 (published online on 18.4.2017), DOI 10.1007/s10107-017-1146-3 .
Abstract
Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed constraint qualifications (CQs) as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible CQs, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive so-called M-stationarity conditions. The strength of assumptions and conclusions in the two forms of the MPEC is strongly related with the CQs on the 'lower level' imposed on the set whose normal cone appears in the generalized equation. For instance, under just the Mangasarian-Fromovitz CQ (a minimum assumption required for this set), the calmness properties of the original and the enhanced perturbation mapping are drastically different. They become identical in the case of a polyhedral set or when adding the Full Rank CQ. On the other hand, the resulting optimality conditions are affected too. If the considered set even satisfies the Linear Independence CQ, both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. A compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions is provided in the main Theorem 4.3. The obtained results are finally applied to MPECs with structured equilibria.

H. Antil, M. Hintermüller, R.H. Nochetto, Th.M. Surowiec, D. Wegner, Finite horizon model predictive control of electrowetting on dielectric with pinning, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 19 (2017), pp. 1--30, DOI 10.4171/IFB/375 .

H. Egger, Th. Kugler, N. Strogies, Parameter identification in a semilinear hyperbolic system, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 33 (2017), pp. 055022/1--055022/25, DOI 10.1088/1361-6420/aa648c .
Abstract
We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigate the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings.

M.H. Farshbaf Shaker, R. Henrion, D. Hömberg, Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 26 (2018), pp. 821--841 (published online on 11.10.2017), DOI 10.1007/s11228-017-0452-5 .
Abstract
Chance constraints represent a popular tool for finding decisions that enforce a robust satisfaction of random inequality systems in terms of probability. They are widely used in optimization problems subject to uncertain parameters as they arise in many engineering applications. Most structural results of chance constraints (e.g., closedness, convexity, Lipschitz continuity, differentiability etc.) have been formulated in a finite-dimensional setting. The aim of this paper is to generalize some of these well-known semi-continuity and convexity properties to a setting of control problems subject to (uniform) state chance constraints.

V. Guigues, R. Henrion, Joint dynamic probabilistic constraints with projected linear decision rules, Optimization Methods & Software, 32 (2017), pp. 1006--1032.
Abstract
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.

S. Hajian, M. Hintermüller, S. Ulbrich, Total variation diminishing schemes in optimal control of scalar conservation laws, IMA Journal of Numerical Analysis, 39 (2019), pp. 105--140 (published online on 14.12.2017), DOI 10.1093/imanum/drx073 .
Abstract
In this paper, optimal control problems subject to a nonlinear scalar conservation law are studied. Such optimal control problems are challenging both at the continuous and at the discrete level since the control-to-state operator poses difficulties as it is, e.g., not differentiable. Therefore discretization of the underlying optimal control problem should be designed with care. Here the discretize-then-optimize approach is employed where first the full discretization of the objective function as well as the underlying PDE is considered. Then, the derivative of the reduced objective is obtained by using an adjoint calculus. In this paper total variation diminishing Runge-Kutta (TVD-RK) methods for the time discretization of such problems are studied. TVD-RK methods, also called strong stability preserving (SSP), are originally designed to preserve total variation of the discrete solution. It is proven in this paper that providing an SSP state scheme, is enough to ensure stability of the discrete adjoint. However requiring SSP for both discrete state and adjoint is too strong. Also approximation properties that the discrete adjoint inherits from the discretization of the state equation are studied. Moreover order conditions are derived. In addition, optimal choices with respect to CFL constant are discussed and numerical experiments are presented.

H. Meinlschmidt, Ch. Meyer, J. Rehberg, Optimal control of the thermistor problem in three spatial dimensions. Part 1: Existence of optimal solutions, SIAM Journal on Control and Optimization, 55 (2017), pp. 2876--2904, DOI 10.1137/16M1072644 .
Abstract
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results.

H. Meinlschmidt, Ch. Meyer, J. Rehberg, Optimal control of the thermistor problem in three spatial dimensions. Part 2: Optimality conditions, SIAM Journal on Control and Optimization, 55 (2017), pp. 2368--2392, DOI 10.1137/16M1072656 .
Abstract
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results.

W. VAN Ackooij, R. Henrion, (Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), pp. 63--87, DOI 10.1137/16M1061308 .
Abstract
We consider probability functions of parameter-dependent random inequality systems under Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential of such probability functions without imposing compactness conditions. A constraint qualification ensuring continuous differentiability is formulated. Explicit formulae are derived from the general result in case of linear random inequality systems. In the case of a constant coefficient matrix an upper estimate for even the smaller Mordukhovich subdifferential is proven.

M. Hintermüller, T. Keil, D. Wegner, Optimal control of a semidiscrete Cahn--Hilliard--Navier--Stokes system with non-matched fluid densities, SIAM Journal on Control and Optimization, 55 (2017), pp. 1954--1989.

M. Hintermüller, C.N. Rautenberg, M. Mohammadi, M. Kanitsar, Optimal sensor placement: A robust approach, SIAM Journal on Control and Optimization, 55 (2017), pp. 3609--3639.
Abstract
We address the problem of optimally placing sensor networks for convection-diffusion processes where the convective part is perturbed. The problem is formulated as an optimal control problem where the integral Riccati equation is a constraint and the design variables are sensor locations. The objective functional involves a term associated to the trace of the solution to the Riccati equation and a term given by a constrained optimization problem for the directional derivative of the previous quantity over a set of admissible perturbations. The paper addresses the existence of the derivative with respect to the convective part of the solution to the Riccati equation, the well-posedness of the optimization problem and finalizes with a range of numerical tests.

M. Hintermüller, C.N. Rautenberg, S. Rösel, Density of convex intersections and applications, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 473 (2017), pp. 20160919/1--20160919/28, DOI 10.1098/rspa.2016.0919 .
Abstract
In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.

M. Eigel, Ch. Merdon, Equilibration a posteriori error estimation for convection-diffusion-reaction problems, Journal of Scientific Computing, 67 (2016), pp. 747--768.
Abstract
We study a posteriori error estimates for convection-diffusion-reaction problems with possibly dominating convection or reaction and inhomogeneous boundary conditions. For the conforming FEM discretisation with streamline diffusion stabilisation (SDM), we derive robust and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of H (div, Ω). Error estimators of this type have become popular recently since they provide guaranteed error bounds without further unknown constants. The estimators can be improved significantly by some postprocessing and divergence correction technique. For an extension of the energy norm by a dual norm of some part of the differential operator, complete independence from the coefficients of the problem is achieved.

Numerical benchmarks illustrate the very good performance of the error estimators in the convection dominated and the singularly perturbed cases.

D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410--423.
Abstract
We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantum-well lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights.

M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Outer limit of subdifferentials and calmness moduli in linear and nonlinear programming, Journal of Optimization Theory and Applications, 169 (2016), pp. 925--952.
Abstract
With a common background and motivation, the main contributions of this paper are developed in two different directions. Firstly, we are concerned with functions which are the maximum of a finite amount of continuously differentiable functions of n real variables, paying attention to the case of polyhedral functions. For these max-functions, we obtain some results about outer limits of subdifferentials, which are applied to derive an upper bound for the calmness modulus of nonlinear systems. When confined to the convex case, in addition, a lower bound on this modulus is also obtained. Secondly, by means of a KKT index set approach, we are also able to provide a point-based formula for the calmness modulus of the argmin mapping of linear programming problems without any uniqueness assumption on the optimal set. This formula still provides a lower bound in linear semi-infinite programming. Illustrative examples are given.

M.J. Cánovas, R. Henrion, J. Parra, F.J. Toledo, Critical objective size and calmness modulus in linear programming, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 24 (2016), pp. 565--579.
Abstract
This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in citeCHPTmp. In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to explore some strategies that can improve the referred upper and lower bounds.

C. Carstensen, M. Eigel, Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes, Computational Methods in Applied Mathematics, 16 (2016), pp. 213--230.
Abstract
A hierarchical a posteriori error estimator for the first-order finite element method (FEM) on a red-refined triangular mesh is presented for the 2D Poisson model problem. Reliability and efficiency with some explicit constant is proved for triangulations with inner angles smaller than or equal to pi/2. The error estimator does not rely on any saturation assumption and is valid even in the pre-asymptotic regime on arbitrarily coarse meshes. The evaluation of the estimator is a simple post-processing of the piecewise linear FEM without any extra solve plus a higher-order approximation term. The results also allows the striking observation that arbitrary local averaging of the primal variable leads to a reliable and efficient error estimation. Several numerical experiments illustrate the performance of the proposed a posteriori error estimator for computational benchmarks.

P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary conditions, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 73 (2016), pp. 195--225, DOI 10.1007/s00245-015-9299-z .
Abstract
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.

P. Colli, G. Gilardi, J. Sprekels, Constrained evolution for a quasilinear parabolic equation, Journal of Optimization Theory and Applications, 170 (2016), pp. 713--734.
Abstract
In the present contribution, a feedback control law is studied for a quasilinear parabolic equation. First, we prove the well-posedness and some regularity results for the Cauchy--Neumann problem for this equation, modified by adding an extra term which is a multiple of the subdifferential of the distance function from a closed convex set K of L²(Ω). Then, we consider convex sets of obstacle or double-obstacle type, and we can act on the factor of the feedback control in order to be able to reach the convex set within a finite time, by proving rigorously this property.

P. Colli, G. Gilardi, J. Sprekels, Distributed optimal control of a nonstandard nonlocal phase field system, AIMS Mathematics, 1 (2016), pp. 246--281.
Abstract
We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, Journal of Differential Equations, 260 (2016), pp. 3397--3447.
Abstract
The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong W^1,2-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.

A. Gasnikov, P. Dvurechensky, Y. Dorn, Y. Maximov, Numerical methods for finding equilibrium flow distribution in Beckman and stable dynamics models, Rossiiskaya Akademiya Nauk. Matematicheskoe Modelirovanie, 28 (2016), pp. 40--64.

H. Meinlschmidt, J. Rehberg, Hölder-estimates for non-autonomous parabolic problems with rough data, Evolution Equations and Control Theory, 5 (2016), pp. 147--184.
Abstract
In this paper we establish Hölder estimates for solutions to non-autonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al., which also serves as the starting point for our investigations.

K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016), pp. 557--588.
Abstract
We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.

M.H. Farshbaf Shaker, C. Hecht, Optimal control of elastic vector-valued Allen--Cahn variational inequalities, SIAM Journal on Control and Optimization, 54 (2016), pp. 129--152.
Abstract
In this paper we consider a elastic vector-valued Allen--Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

S.P. Frigeri, E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal Cahn--Hilliard/Navier--Stokes system in two dimensions, SIAM Journal on Control and Optimization, 54 (2016), pp. 221 -- 250.
Abstract
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier-Stokes system with a convective nonlocal Cahn-Hilliard equation in two dimensions of space. We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.

CH. Heinemann, K. Sturm, Shape optimisation for a class of semilinear variational inequalities with applications to damage models, SIAM Journal on Mathematical Analysis, 48 (2016), pp. 3579--3617, DOI 10.1137/16M1057759 .
Abstract
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise from another optimisation problems. We prove a strong convergence property for the material derivative and establish state-shape derivatives under regularity assumptions. Finally, as a concrete application from continuum mechanics, we show how the dynamic obstacle case can be used to treat shape optimisation problems for time-discretised brittle damage models for elastic solids. We derive a necessary optimality system for optimal shapes whose state variables approximate desired damage patterns and/or displacement fields.

M. Hintermüller, Th. Surowiec, A bundle-free implicit programming approach for a class of elliptic MPECs in function space, Mathematical Programming Series A, 160 (2016), pp. 271--305.

E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal convective Cahn--Hilliard equation by the velocity in three dimensions, SIAM Journal on Control and Optimization, 53 (2015), pp. 1654--1680.
Abstract
In this paper we study a distributed optimal control problem for a nonlocal convective Cahn-Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system of PDEs containing singular and degenerating terms, and the control variable, which is given by the velocity of the motion occurring in the convective term, is nonlinearly coupled to the state variable. The latter fact makes it necessary to state rather special regularity assumptions for the admissible controls, which, while looking a bit nonstandard, are however quite natural in the corresponding analytical framework. In fact, they are indispensable prerequisites to guarantee the well-posedness of the associated state system. In this contribution, we employ recently proved existence, uniqueness and regularity results for the solution to the associated state system in order to establish the existence of optimal controls and appropriate first-order necessary optimality conditions for the optimal control problem.

P.-É. Druet, Some mathematical problems related to the second order optimal shape of a crystallization interface, Discrete and Continuous Dynamical Systems, 35 (2015), pp. 2443--2463.
Abstract
We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solid-liquid interface in a two-phase system subject to a temperature gradient. The interface satisfies the minimization principle of the free energy, while the temperature is solving the heat equation with a radiation boundary conditions at the outer wall. Under the condition that the temperature gradient is uniformly negative in the direction of crystallization, the interface is expected to have a global graph representation. We reformulate this condition as a pointwise constraint on the gradient of the state, and we derive the first order optimality system for a class of objective functionals that account for the second surface derivatives, and for the surface temperature gradient.

M. Eigel, D. Peterseim, Simulation of composite materials by a Network FEM with error control, Computational Methods in Applied Mathematics, 15 (2015), pp. 21--37.
Abstract
A novel Finite Element Method (FEM) for the computational simulation in particle reinforced composite materials with many inclusions is presented. It is based on a specially designed mesh consisting of triangles and channel-like connections between inclusions which form a network structure. The total number of elements and, hence, the number of degrees of freedom are proportional to the number of inclusions. The error of the method is independent of the possibly tiny distances of neighbouring inclusions.

We present algorithmic details for the generation of the problem adapted mesh and derive an efficient residual a posteriori error estimator which enables to compute reliable upper and lower error bounds. Several numerical examples illustrate the performance of the method and the error estimator. In particular, it is demonstrated that the (common) assumption of a lattice structure of inclusions can easily lead to incorrect predictions about material properties.

P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the pure Cahn--Hilliard equation with dynamic boundary conditions, Advances in Nonlinear Analysis, 4 (2015), pp. 311--325.
Abstract
A boundary control problem for the pure Cahn--Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.

P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Optimal boundary control of a viscous Cahn--Hilliard system with dynamic boundary condition and double obstacle potentials, SIAM Journal on Control and Optimization, 53 (2015), pp. 2696--2721.
Abstract
In this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) Allen--Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary conditions, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 7 (2015), pp. 41--66.
Abstract
In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn--Hilliard equation with possibly singular potentials and dynamic boundary conditions.

P. Colli, M.H. Farshbaf Shaker, J. Sprekels, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 71 (2015), pp. 1--24.
Abstract
In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

P. Colli, J. Sprekels, Optimal control of an Allen--Cahn equation with singular potentials and dynamic boundary condition, SIAM Journal on Control and Optimization, 53 (2015), pp. 213--234.
Abstract
In this paper, we investigate optimal control problems for Allen--Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace--Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. Parabolic problems with nonlinear dynamic boundary conditions involving the Laplace--Beltrami operation have recently drawn increasing attention due to their importance in applications, while their optimal control was apparently never studied before. In this paper, we first extend known well-posedness and regularity results for the state equation and then show the existence of optimal controls and that the control-to-state mapping is twice continuously Fréchet differentiable between appropriate function spaces. Based on these results, we establish the first-order necessary optimality conditions in terms of a variational inequality and the adjoint state equation, and we prove second-order sufficient optimality conditions.

G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Discrete approximations of a controlled sweeping process, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 23 (2015), pp. 69--86.

W. Giese, M. Eigel, S. Westerheide, Ch. Engwer, E. Klipp, Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models, Physical Biology, 12 (2015), pp. 066014/1--066014/18.
Abstract
In silico experiments bear the potential to further the understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results for the chosen models. We consider cell polarization and spatial reorganization of membrane proteins which are fundamental for cell division, chemotaxis and morphogenesis. Our computational study is motivated by mating and budding processes of S. cerevisiae. In these processes a key player during the initial phase of polarization is the GTPase Cdc42 which occurs in an active membrane-bound form and an inactive cytosolic form. We use partial differential equations to describe the membrane-cytosol shuttling of Cdc42 during budding as well as mating of yeast. The membrane is modeled as a thin layer that only allows lateral diffusion and the cytosol is modeled as a volume. We investigate how cell shape and diffusion barriers like septin structures or bud scars influence Cdc42 cluster formation and subsequent polarization of the yeast cell. Since the details of the binding kinetics of cytosolic proteins to the membrane are still controversial, we employ two conceptual models which assume different binding kinetics. An extensive set of in silico experiments with different modeling hypotheses illustrate the qualitative dependence of cell polarization on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. We examine that spatial inhomogenities essentially determine the location of Cdc42 cluster formation and spatial properties are crucial for the realistic description of the polarization process in cells. In particular, our computer simulations suggest that diffusion barriers are essential for the yeast cell to grow a protrusion.

P. Dvurechensky, Y. Nesterov, V. Spokoiny, Primal-dual methods for solving infinite-dimensional games, Journal of Optimization Theory and Applications, 166 (2015), pp. 23--51.

M.H. Farshbaf Shaker, A relaxation approach to vector-valued Allen--Cahn MPEC problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 72 (2015), pp. 325--351.

M.H. Farshbaf Shaker, Ch. Heinemann, A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media, Mathematical Models & Methods in Applied Sciences, 25 (2015), pp. 2749--2793.
Abstract
In this work we investigate a phase field model for damage processes in two-dimensional viscoelastic media with nonhomogeneous Neumann data describing external boundary forces. In the first part we establish global-in-time existence, uniqueness, a priori estimates and continuous dependence of strong solutions on the data. The main difficulty is caused by the irreversibility as well as boundedness of the phase field variable which results in a doubly constrained PDE system. In the last part we consider an optimal control problem where a cost functional penalizes maximal deviations from prescribed damage profiles. The goal is to minimize the cost functional with respect to exterior forces acting on the boundary which play the role of the control variable in the considered model . To this end, we prove existence of minimizers and study a family of “local” approximations via adapted cost functionals.

TH. Arnold, R. Henrion, A. Möller, S. Vigerske, A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints, Pacific Journal of Optimization. An International Journal, 10 (2014), pp. 5--20.
Abstract
We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.

M. Eigel, T. Samrowski, Functional a posteriori error estimation for stationary reaction-convection-diffusion problems, Computational Methods in Applied Mathematics, 14 (2014), pp. 135--150.
Abstract
A functional type a posteriori error estimator for the finite element discretisation of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimisation problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator and compare it with some classic a posteriori error estimators often used in practice. It is observed that the new estimator exhibits a good efficiency also with convection-dominated problem settings.

K. Emich, R. Henrion, W. Römisch, Conditioning of linear-quadratic two-stage stochastic optimization problems, Mathematical Programming. A Publication of the Mathematical Programming Society, 148 (2014), pp. 201--221.
Abstract
In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number can be estimated from above explicitly in terms of the problem data by applying appropriate calculus rules. Here, a chain rule for the extended partial second-order subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role. The obtained results are illustrated for the example of two-stage stochastic optimization problems with simple recourse.

K. Emich, R. Henrion, A simple formula for the second-order subdifferential of maximum functions, Vietnam Journal of Mathematics, 42 (2014), pp. 467--478.
Abstract
We derive a simple formula for the second-order subdifferential of the maximum of coordinates which allows us to construct this set immediately from its argument and the direction to which it is applied. This formula can be combined with a chain rule recently proved by Mordukhovich and Rockafellar [9] in order to derive a similarly simple formula for the extended partial second-order subdifferential of finite maxima of smooth functions. Analogous formulae can be derived immediately for the full and conventional partial second-order subdifferentials.

R. Hildebrand, Hessian potentials with parallel derivatives, Results in Mathematics, 65 (2014), pp. 399--413.

R. Hildebrand, Minimal zeros of copositive matrices, Linear Algebra and its Applications, 459 (2014), pp. 154--174.
Abstract
Let A be an element of the copositive cone CnCn. A zero u of A is a nonzero nonnegative vector such that uTAu=0uTAu=0. The support of u is the index set View the MathML sourcesuppu?1,?,n corresponding to the positive entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u . We investigate the properties of minimal zeros of copositive matrices and their supports. Special attention is devoted to copositive matrices which are irreducible with respect to the cone S+(n)S+(n) of positive semi-definite matrices, i.e., matrices which cannot be written as a sum of a copositive and a nonzero positive semi-definite matrix. We give a necessary and sufficient condition for irreducibility of a matrix A with respect to S+(n)S+(n) in terms of its minimal zeros. A similar condition is given for the irreducibility with respect to the cone NnNn of entry-wise nonnegative matrices. For n=5n=5 matrices which are irreducible with respect to both S+(5)S+(5) and N5N5 are extremal. For n=6n=6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided.

L. Blank, M.H. Farshbaf Shaker, H. Garcke, V. Styles, Relating phase field and sharp interface approaches to structural topology optimization, ESAIM. Control, Optimisation and Calculus of Variations, 20 (2014), pp. 1025--1058.
Abstract
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014), pp. 1328--1333.
Abstract
In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.

A. Fügenschuh, B. Geissler, Ch. Hayn, R. Henrion, B. Hiller, J. Humpola, Th. Koch ET AL., Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets, Energy Systems, 5 (2014), pp. 449--473.

W. VAN Ackooij, R. Henrion, Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussian-like distributions, SIAM Journal on Optimization, 24 (2014), pp. 1864--1889.
Abstract
Probabilistic constraints represent a major model of stochastic optimization. A possible approach for solving probabilistically constrained optimization problems consists in applying nonlinear programming methods. In order to do so, one has to provide sufficiently precise approximations for values and gradients of probability functions. For linear probabilistic constraints under Gaussian distribution this can be successfully done by analytically reducing these values and gradients to values of Gaussian distribution functions and computing the latter, for instance, by Genz' code. For nonlinear models one may fall back on the spherical-radial decomposition of Gaussian random vectors and apply, for instance, Deák's sampling scheme for the uniform distribution on the sphere in order to compute values of corresponding probability functions. The present paper demonstrates how the same sampling scheme can be used in order to simultaneously compute gradients of these probability functions. More precisely, we prove a formula representing these gradients in the Gaussian case as a certain integral over the sphere again. Later, the result is extended to alternative distributions with an emphasis on the multivariate Student (or T-) distribution.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in non-isothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014), pp. 035003/1--035003/24.
Abstract
We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.

P. Colli, G. Gilardi, P. Podio-Guidugli, J. Sprekels, An asymptotic analysis for a nonstandard Cahn--Hilliard system with viscosity, Discrete and Continuous Dynamical Systems -- Series S, 6 (2013), pp. 353--368.
Abstract
This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order parameter $rho$ and the chemical potential $mu$; each equation includes a viscosity term -- respectively, $varepsilon,partial_tmu$ and $delta,partial_trho$ -- with $varepsilon$ and $delta$ two positive parameters; the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In a recent paper [5], we proved that this problem is well-posed and investigated the long-time behavior of its $(varepsilon,delta)-$solutions. Here we discuss the asymptotic limit of the system as $eps$ tends to 0. We prove convergence of $(varepsilon,delta)-$solutions to the corresponding solutions for the case $eps$ =0, whose long-time behavior we characterize; in the proofs, we employ compactness and monotonicity arguments.

K. Krumbiegel, J. Rehberg, Second order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints, SIAM Journal on Control and Optimization, 51 (2013), pp. 301--331.
Abstract
In this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.

R. Henrion, A. Kruger, J. Outrata, Some remarks on stability of generalized equations, Journal of Optimization Theory and Applications, 159 (2013), pp. 681--697.
Abstract
The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by $C^2$ inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian-Fromovitz and the Constant Rank qualification conditions. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.

D. Hömberg, K. Krumbiegel, J. Rehberg, Optimal control of a parabolic equation with dynamic boundary condition, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 67 (2013), pp. 3--31.
Abstract
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the Robin boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an $L^p$ function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.

P. Colli, G. Gilardi, P. Podio-Guidugli, J. Sprekels, Distributed optimal control of a nonstandard system of phase field equations, Continuum Mechanics and Thermodynamics, 24 (2012), pp. 437--459.
Abstract
We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been introduced recently in [4], on the basis of the theory developed in [15], and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

P. Colli, G. Gilardi, J. Sprekels, Analysis and optimal boundary control of a nonstandard system of phase field equations, Milan Journal of Mathematics, 80 (2012), pp. 119--149.
Abstract
We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in Podio-Guidugli (2006), describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in Colli, Gilardi, Podio-Guidugli, and Sprekels (2011a and b) for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.

G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process, Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, 19 (2012), pp. 117--159.

M. Gerdts, R. Henrion, D. Hömberg, Ch. Landry, Path planning and collision avoidance for robots, Numerical Algebra, Control and Optimization, 2 (2012), pp. 437--463.
Abstract
An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.

R. Henrion, J. Outrata, Th. Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market, ESAIM. Control, Optimisation and Calculus of Variations, 18 (2012), pp. 295--317.
Abstract
We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called $M$-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify $M$-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration.

W. Dreyer, P.-É. Druet, O. Klein, J. Sprekels, Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals, Milan Journal of Mathematics, 80 (2012), pp. 311--332.
Abstract
This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.

R. Henrion, J. Outrata, Th. Surowiec, On regular coderivatives in parametric equilibria with non-unique multiplier, Mathematical Programming. A Publication of the Mathematical Programming Society, 136 (2012), pp. 111--131.

K. Krumbiegel, I. Neitzel, A. Rösch, Regularization error estimates for semilinear elliptic optimal control problems with pointwise state and control constraints, Computational Optimization and Applications. An International Journal, 52 (2012), pp. 181--207.
Abstract
In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. A sufficient second order optimality condition and uniqueness of the dual variables are assumed for that problem. Sufficient second order optimality conditions are shown for regularized problems with small regularization parameter. Moreover, error estimates with respect to the regularization parameter are derived.

P.-É. Druet, O. Klein, J. Sprekels, F. Tröltzsch, I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects, SIAM Journal on Control and Optimization, 49 (2011), pp. 1707--1736.
Abstract
The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established.

R. Henrion, Th. Surowiec, On calmness conditions in convex bilevel programming, Applicable Analysis. An International Journal, 90 (2011), pp. 951--970.
Abstract
In this article we compare two different calmness conditions which are widely used in the literature on bilevel programming and on mathematical programs with equilibrium constraints. In order to do so, we consider convex bilevel programming as a kind of intersection between both research areas. The so-called partial calmness concept is based on the function value approach for describing the lower level solution set. Alternatively, calmness in the sense of multifunctions may be considered for perturbations of the generalized equation representing the same lower level solution set. Both concepts allow to derive first order necessary optimality conditions via tools of generalized differentiation introduced by Mordukhovich. They are very different, however, concerning their range of applicability and the form of optimality conditions obtained. The results of this paper seem to suggest that partial calmness is considerably more restrictive than calmness of the perturbed generalized equation. This fact is also illustrated by means of a dicretized obstacle control problem.

R. Henrion, C. Strugarek, Convexity of chance constraints with dependent random variables: The use of copulae, International Series in Operations Research & Management Science, 163 (2011), pp. 427--439.

J. Sprekels, D. Tiba, Extensions of the control variational method, Control and Cybernetics, 40 (2011), pp. 1099--1108.
Abstract
The control variational method is a development of the variational approach, based on optimal control theory. In this work, we give an application to a variational inequality arising in mechanics and involving unilateral conditions both in the domain and on the boundary, and we explore the extension of the method to time-dependent problems.

A. Caboussat, Ch. Landry, J. Rappaz, Optimization problem coupled with differential equations: A numerical algorithm mixing an interior-point method and event detection, Journal of Optimization Theory and Applications, 147 (2010), pp. 141--156.

M.J. Fabian, R. Henrion, A.Y. Kruger, J. Outrata, Error bounds: Necessary and sufficient conditions, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 121--149.
Abstract
The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

R. Henrion, B. Mordukhovich, N.M. Nam, Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM Journal on Optimization, 20 (2010), pp. 2199--2227.

R. Henrion, J. Outrata, Th. Surowiec, A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints, Kybernetika. The Journal of the Czech Society for Cybernetics and Information Sciences. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague. English., 46 (2010), pp. 423--434.
Abstract
In this paper, we consider the characterization of strong stationary solutions to equilibrium problems with equilibrium constraints (EPECs). Assuming that the underlying generalized equation satisfies strong regularity in the sense of Robinson, an explicit multiplier-based stationarity condition can be derived. This is applied then to an equilibrium model arising from ISO-regulated electricity spot markets.

R. Henrion, W. Römisch, Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions, Annals of Operations Research, 177 (2010), pp. 115--125.

R. Henrion, A. Seeger, Inradius and circumradius of various convex cones arising in applications, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 483--511.

D. Hömberg, Ch. Meyer, J. Rehberg, W. Ring, Optimal control for the thermistor problem, SIAM Journal on Control and Optimization, 48 (2010), pp. 3449--3481.
Abstract
This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem.

K. Krumbiegel, Ch. Meyer, A. Rösch, A priori error analysis for linear quadratic elliptic Neumann boundary control problems with control and state constraints, SIAM Journal on Control and Optimization, 48 (2010), pp. 5108--5142.

K. Krumbiegel, I. Neitzel, A. Rösch, Sufficient optimality conditions for the Moreau--Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 2 (2010), pp. 222--246.
Abstract
We develop sufficient optimality conditions for a Moreau-Yosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept, for which standard second order sufficient conditions have been shown. Moreover, we compare both regularization approaches within a numerical example.

R. Henrion, A. Seeger, On properties of different notions of centers for convex cones, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 205--231.

R. Henrion, Ch. Küchler, W. Römisch, Scenario reduction in stochastic programming with respect to discrepancy distances, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 67--93.

R. Henrion, J. Outrata, Th. Surowiec, On the co-derivative of normal cone mappings to inequality systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 71 (2009), pp. 1213--1226.
Abstract
The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both, the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constraint Qualification satisfied) case are considered. A major part of the results relies on general transformation formulae previously obtained by Mordukhovich and Outrata. This allows to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by Mordukhovich and Outrata applies, however a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. A series of examples illustrates the use and comparison of the presented formulae.

D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009), pp. 438--442.
Abstract
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.

D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009), pp. 669--681.
Abstract
The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solid-solid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results.

K. Krumbiegel, A. Rösch, A virtual control concept for state constrained optimal control problems, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 213--233.

J. Sprekels, D. Tiba, The control variational approach for differential systems, SIAM Journal on Control and Optimization, 47 (2009), pp. 3220--3236.

P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008), pp. 793--799.
Abstract
The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations.

R. Henrion, Ch. Küchler, W. Römisch, Discrepancy distances and scenario reduction in two-stage stochastic integer programming, Journal of Industrial and Management Optimization, 4 (2008), pp. 363--384.

R. Henrion, J. Outrata, On calculating the normal cone to a finite union of convex polyhedra, Optimization. A Journal of Mathematical Programming and Operations Research, 57 (2008), pp. 57--78.

R. Henrion, A. Seeger, Uniform boundedness of norms of convex and nonconvex processes, Numerical Functional Analysis and Optimization. An International Journal, 29 (2008), pp. 551--573.

R. Henrion, C. Strugarek, Convexity of chance constraints with independent random variables, Computational Optimization and Applications. An International Journal, 41 (2008), pp. 263--276.

D. Dentcheva, R. Henrion, A. Ruszczynski, Stability and sensitivity of optimization problems with first order stochastic dominance constraints, SIAM Journal on Optimization, 18 (2007), pp. 322--337.

C. Lefter, J. Sprekels, Optimal boundary control of a phase field system modeling nonisothermal phase transitions, Advances in Mathematical Sciences and Applications, 17 (2007), pp. 181-194.

R. Henrion, W. Römisch, On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling, Applications of Mathematics, 522 (2007), pp. 473--494.
Abstract
Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata [17]. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived (Proposition 3.2). Later the co-derivative formula is used for verifying constraint qualifications and for identifying M-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.

R. Henrion, Structural properties of linear probabilistic constraints, Optimization. A Journal of Mathematical Programming and Operations Research, 56 (2007), pp. 425--440.

R. Henrion, A. Lewis, A. Seeger, Distance to uncontrollability for convex processes, SIAM Journal on Optimization, 45 (2006), pp. 26--50.

R. Henrion, Some remarks on value-at-risk optimization, International Journal of Management Science and Engineering Management, 1 (2006), pp. 111--118.

V. Arnăutu, J. Sprekels, D. Tiba, Optimization problems for curved mechanical structures, SIAM Journal on Control and Optimization, 44 (2005), pp. 743--775.

R. Henrion, J. Outrata, Calmness of constraint systems with applications, Mathematical Programming. A Publication of the Mathematical Programming Society, 104 (2005), pp. 437--464.

P. Bosch, A. Jourani, R. Henrion, Sufficient conditions for error bounds and applications, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 50 (2004), pp. 161--181.

R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Mathematical Programming. A Publication of the Mathematical Programming Society, 100 (2004), pp. 589--611.

R. Henrion, A. Möller, Optimization of a continuous distillation process under random inflow rate, Computers & Mathematics with Applications. An International Journal, 45 (2003), pp. 247--262.

D. Hömberg, J. Sokolowski, Optimal shape design of inductor coils for induction hardening, SIAM Journal on Control and Optimization, 42 (2003), pp. 1087--1117.

D. Hömberg, S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003), pp. 1003-1028.

J. Sprekels, D. Tiba, Optimization of clamped plates with discontinuous thickness, Systems & Control Letters, 48 (2003), pp. 289-295.

A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches, SIAM Journal on Control and Optimization, 40 (2001), pp. 1107-1133.

V. Arnăutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 337--354.

J. Sprekels, D. Tiba, Sur les arches lipschitziennes, Comptes Rendus Mathematique. Academie des Sciences. Paris, 331 (2000), pp. 179--184.

A. Alphonse, M. Hintermüller, C.N. Rautenberg, Recent trends and views on elliptic quasi-variational inequalities, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 1--31.

P. Colli, G. Gilardi, J. Sprekels, Nonlocal phase field models of viscous Cahn--Hilliard type, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 71--100, DOI 10.1007/978-3-030-33116-0 .
Abstract
A nonlocal phase field model of viscous Cahn--Hilliard type is considered. This model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The resulting system of differential equations consists of a highly nonlinear parabolic equation coupled to a nonlocal ordinary differential equation, which has singular terms that render the analysis difficult. Some results are presented on the well-posedness and stability of the system as well as on the distributed optimal control problem.

M. Hintermüller, N. Strogies, On the consistency of Runge--Kutta methods up to order three applied to the optimal control of scalar conservation laws, in: Numerical Analysis and Optimization, M. Al-Baali, L. Grandinetti, A. Purnama, eds., 235 of Springer Proceedings in Mathematics & Statistics, Springer Nature Switzerland AG, Cham, 2019, pp. 119--154.
Abstract
Higher-order Runge-Kutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RK-coefficients are derived that coincide with those characterizing strong stability preserving Runge-Kutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a third-order method. Finally, numerical tests for controlling Burgers equation validate the theoretical results.

M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Indexation strategies and calmness constants for uncertain linear inequality systems, in: The Mathematics of the Uncertain, E. Gil, E. Gil, J. Gil, M.Á. Gil, eds., 142 of Studies in Systems, Decision and Control, Springer, 2018, pp. 831--843.

P. Dvurechensky, A. Gasnikov, A. Kroshnin, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, in: Proceedings of the 35th International Conference on Machine Learning, J. Dy, A. Krause, eds., 80 of Proceedings of Machine Learning Research, 2018, pp. 1367--1376.

M. Hintermüller, T. Keil, Some recent developments in optimal control of multiphase flows, in: Shape Optimization, Homogenization and Optimal Control. DFG-AIMS Workshop held at the AIMS Center Senegal, March 13--16, 2017, V. Schulz, D. Seck, eds., 169 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2018, pp. 113--142, DOI 10.1007/978-3-319-90469-6_7 .

P. Colli, J. Sprekels, Optimal boundary control of a nonstandard Cahn--Hilliard system with dynamic boundary condition and double obstacle inclusions, in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., 22 of Springer INdAM Series, Springer International Publishing AG, Cham, 2017, pp. 151--182, DOI 10.1007/978-3-319-64489-9 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P.Podio-Guidugli in Ric. Mat. 55 (2006), pp.105-118. The model consists of a strongly coupled system of nonlinear parabolic differential inclusions, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically; the system is complemented by initial and boundary conditions. For the order parameter of the phase separation process, a dynamic boundary condition involving the Laplace-Beltrami operator is assumed, which models an additional nonconserving phase transition occurring on the surface of the domain. We complement in this paper results that were established in the recent contribution appeared in Evol. Equ. Control Theory 6 (2017), pp. 35-58, by the two authors and Gianni Gilardi. In contrast to that paper, in which differentiable potentials of logarithmic type were considered, we investigate here the (more difficult) case of nondifferentiable potentials of double obstacle type. For such nonlinearities, the standard techniques of optimal control theory to establish the existence of Lagrange multipliers for the state constraints are known to fail. To overcome these difficulties, we employ the following line of approach: we use the results contained in the preprint arXiv:1609.07046 [math.AP] (2016), pp. 1-30, for the case of (differentiable) logarithmic potentials and perform a so-called "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials.

P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on nonuniform 1D grids, in: Finite Volumes for Complex Applications VIII -- Methods and Theoretical Aspects, FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing AG, Cham, 2017, pp. 303--310.

A. Anikin, A. Gasnikov, A. Garinov, P. Dvurechensky, V. Semenov, Parallelizable dual methods for searching equilibriums in large-scale mixed traffic assignment problems (in Russian), in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 85--89.

A. Chernov, P. Dvurechensky, A primal-dual first-order method for minimization problems with linear constraints, in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 41--45.

P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, in: Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016), A. Kononov, I. Bykadorov , O. Khamisov , I. Davydov , P. Kononova , eds., 1623 of CEUR Workshop Proceedings, Technische Universität Aaachen, pp. 584--595.

CH. Landry, M. Gerdts, R. Henrion, D. Hömberg, W. Welz, Collision-free path planning of welding robots, in: Progress in Industrial Mathematics at ECMI 2012, M. Fontes, M. Günther, N. Marheineke, eds., 19 of Mathematics in Industry, Springer, Cham et al., 2014, pp. 251--256.

L. Blank, M.H. Farshbaf Shaker, C. Hecht, J. Michl, Ch. Rupprecht, Optimal control of Allen--Cahn systems, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 11--26.

L. Blank, M.H. Farshbaf Shaker, H. Garcke, Ch. Rupprecht, V. Styles, Multi-material phase field approach to structural topology optimization, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 231--246.

T. Bosse, R. Henrion, D. Hömberg, Ch. Landry, H. Leövey ET AL., C2 -- Nonlinear programming with applications to production processes, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 171--187.

C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C -- Production, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151--153.

M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4 -- PDE-constrained optimization with industrial applications, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207--222.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227--243.

O. Klein, J. Sprekels, SHOWCASE 13 -- Growth of semiconductor bulk single crystals, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 224--225.

CH. Landry, W. Welz, R. Henrion, D. Hömberg, M. Skutella, Task assignment, sequencing and path-planning in robotic welding cells, Methods and Models in Automation and Robotics (MMAR), 2013 -- 18th International Conference on, Miedzyzdroje, Poland, August 26 - 29, 2013, IEEE, 2013, pp. 252--257.
Abstract
A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collision-free paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently.

K. Chełminski, D. Hömberg, O. Rott, Coupling of process, machine, and work-piece in production processes: A challenge for industrial mathematics, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18 - 19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 57--75.

D. Hömberg, D. Kern, PDE-constrained control problems related to the heat treatment of steel, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18 - 19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 35--46.

M.J. Fabian, R. Henrion, A. Kruger, J. Outrata, About error bounds in metric spaces, D. Klatte, H.-J. Lüthi, K. Schmedders, eds., Operations Research Proceedings 2011, Springer, Berlin Heidelberg, 2012, pp. 33--38.

R. Henrion, Optimization under uncertainty (Models and basic properties), in: Wiley Encyclopedia of Operations Research and Management Science, J.J. Cochran, L.A. Cox, P. Keskinocak ET AL., eds., 5, Wiley, New York, 2011, pp. 3334--3341.

D. Kern, Die Welt des Herrn Kuhn, in: Besser als Mathe --- Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. Lutz-Westphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 141--150.

H. Heitsch, R. Henrion, Ch. Küchler, W. Römisch, Generierung von Szenariobäumen und Szenarioreduktion für stochastische Optimierungsprobleme in der Energiewirtschaft, in: Dezentrale regenerative Energieversorgung: Innovative Modellierung und Optimierung, R. Schultz, H.-J. Wagner, eds., LIT Verlag, Münster, 2009, pp. 227--254.

D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering -- IDE 2008, 17--19 September 2008, Bremen, Germany, H.-W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201--209.

CH. Meyer, D. Hömberg, J. Rehberg, W. Ring, Optimal control of the thermistor problem, in: Optimal Control of Coupled Systems of PDE, Workshop, March 2--8, 2008, 5 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2008, pp. 624-626.

D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, in: Distortion Engineering -- Verzugsbeherrschung in der Fertigung III --, 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 39--55.

J. Sprekels, D. Tiba, Chapter 18: Optimal Design of Mechanical Structures, in: Control Theory of Partial Differential Equations (proceedings of the conference held at Georgetown University, May 30 -- June 1, 2003), O. Imanuvilov, G. Leugering, R. Triggiani, B. Zhang, eds., 242 of Lecture Notes in Pure and Applied Mathematics, Chapman & Hall / CRC, Boca Raton, Florida, 2005, pp. 259-271.

R. Henrion, Perturbation analysis of chance-constrained programs under variation of all constraint data, in: Dynamic Stochastic Optimization, K. Marti, ed., 532 of Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg, 2004, pp. 257--274.

D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325--335.

J. Sprekels, O. Klein, P. Philip, K. Wilmanski, Optimal control of sublimation growth of SiC crystals, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 334--343.

J. Sprekels, D. Tiba, Optimization of differential systems with hysteresis, in: Analysis and Optimization of Differential Systems, IFIP TC7/WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10--14, 2002, Constanta, Romania, V. Barbu, I. Lasiecka, D. Tiba, C. Varsan, eds., Kluwer Academic Publishers, Boston, 2003, pp. 387--398.

J. Sprekels, D. Tiba, Control variational methods for differential equations, in: Optimal Control of Complex Structures, K.-H. Hoffmann, I. Lasiecka, G. Leugering, J.a.T.F. Sprekels, eds., 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, pp. 245-257.

M.S. Aronna, J.F. Bonnans, A. Kröner, State-constrained control-affine parabolic problems II: Second order sufficient optimality conditions, Preprint no. 2778, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2778 .
Abstract, PDF (319 kByte)
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform.

P. Colli, A. Signori, J. Sprekels, Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis, Preprint no. 2770, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2770 .
Abstract, PDF (451 kByte)
This paper concerns a distributed optimal control problem for a tumor growth model of Cahn--Hilliard type including chemotaxis with possibly singular anpotentials, where the control and state variables are nonlinearly coupled. First, we discuss the weak well-posedness of the system under very general assumptions for the potentials, which may be singular and nonsmooth. Then, we establish the strong well-posedness of the system in a reduced setting, which however admits the logarithmic potential: this analysis will lay the foundation for the study of the corresponding optimal control problem. Concerning the optimization problem, we address the existence of minimizers and establish both first-order necessary and second-order sufficient conditions for optimality. The mathematically challenging second-order analysis is completely performed here, after showing that the solution mapping is twice continuously differentiable between suitable Banach spaces via the implicit function theorem. Then, we completely identify the second-order Fréchet derivative of the control-to-state operator and carry out a thorough and detailed investigation about the related properties.

M. Hintermüller, S.-M. Stengl, On the convexity of optimal control problems involving non-linear PDEs or VIs and applications to Nash games, Preprint no. 2759, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2759 .
Abstract, PDF (381 kByte)
Generalized Nash equilibrium problems in function spaces involving PDEs are considered. One of the central issues arising in this context is the question of existence, which requires the topological characterization of the set of minimizers for each player of the associated Nash game. In this paper, we propose conditions on the operator and the functional that guarantee the reduced formulation to be a convex minimization problem. Subsequently, we generalize results of convex analysis to derive optimality systems also for non-smooth operators. Our theoretical findings are illustrated by examples.

M. Kantner, Th. Koprucki, Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions, Preprint no. 2748, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2748 .
Abstract, PDF (3116 kByte)
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.

P. Colli, M.H. Farshbaf Shaker, K. Shirakawa, N. Yamazaki, Optimal control for shape memory alloys of the one-dimensional Frémond model, Preprint no. 2737, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2737 .
Abstract, PDF (700 kByte)
In this paper, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems.

P. Colli, G. Gilardi, J. Sprekels, Optimal control of a phase field system of Caginalp type with fractional operators, Preprint no. 2725, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2725 .
Abstract, PDF (360 kByte)
In their recent work “Well-posedness, regularity and asymptotic analyses for a fractional phase field system” (Asymptot. Anal. 114 (2019), 93--128), two of the present authors have studied phase field systems of Caginalp type, which model nonconserved, nonisothermal phase transitions and in which the occurring diffusional operators are given by fractional versions in the spectral sense of unbounded, monotone, selfadjoint, linear operators having compact resolvents. In this paper, we complement this analysis by investigating distributed optimal control problems for such systems. It is shown that the associated control-to-state operator is Fréchet differentiable between suitable Banach spaces, and meaningful first-order necessary optimality conditions are derived in terms of a variational inequality and the associated adjoint state variables.

J. Sprekels, F. Tröltzsch, Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth, Preprint no. 2721, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2721 .
Abstract, PDF (326 kByte)
In this paper, we study an optimal control problem for a nonlinear system of reaction-diffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally introduced in [13]. The model takes the effect of chemotaxis into account but neglects velocity contributions. The unknown quantities of the governing state equations are the chemical potential, the (normalized) tumor fraction, and the nutrient extra-cellular water concentration. The equation governing the evolution of the tumor fraction is dominated by the variational derivative of a double-well potential which may be of singular (e.g., logarithmic) type. In contrast to the recent paper [10] on the same system, we consider in this paper sparsity effects, which means that the cost functional contains a nondifferentiable (but convex) contribution like the L¹-norm. For such problems, we derive first-order necessary optimality conditions and conditions for directional sparsity, both with respect to space and time, where the latter case is of particular interest for practical medical applications in which the control variables are given by the administration of cytotoxic drugs or by the supply of nutrients. In addition to these results, we prove that the corresponding control-to-state operator is twice continuously differentiable between suitable Banach spaces, using the implicit function theorem. This result, which complements and sharpens a differentiability result derived in [10], constitutes a prerequisite for a future derivation of second-order sufficient optimality conditions.

M. Eigel, P. Trunschke, R. Schneider, Convergence bounds for empirical nonlinear least-squares, Preprint no. 2714, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2714 .
Abstract, PDF (4747 kByte)
We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2 norm for which only a weighted Monte Carlo estimate can be computed. The objective is to obtain an approximation of an unknown target function by minimizing the empirical norm. In the case of linear subspaces it is well-known that such least squares approximations can become inaccurate and unstable when the number of samples is too close to the number of parameters. We review this statement for general nonlinear subsets and establish error bounds for the empirical best approximation error. Our results are based on a restricted isometry property (RIP) which holds in probability and we show sufficient conditions for the RIP to be satisfied with high probability. Several model classes are examined where analytical statements can be made about the RIP. Numerical experiments illustrate some of the obtained stability bounds.

D. Kamzolov, A. Gasnikov, P. Dvurechensky, On the optimal combination of tensor optimization methods, Preprint no. 2710, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2710 .
Abstract, PDF (284 kByte)
We consider the minimization problem of a sum of a number of functions having Lipshitz p -th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain near-optimal oracle complexity for each function in the sum separately, meaning, in particular, that the oracle for a function with lower Lipschitz constant is called a smaller number of times. As a building block, we extend the current theory of tensor methods and show how to generalize near-optimal tensor methods to work with inexact tensor step. Further, we investigate the situation when the functions in the sum have Lipschitz derivatives of a different order. For this situation, we propose a generic way to separate the oracle complexity between the parts of the sum. Our method is not optimal, which leads to an open problem of the optimal combination of oracles of a different order.

F. Stonyakin, A. Gasnikov, A. Tyurin, D. Pasechnyuk, A. Agafonov, P. Dvurechensky, D. Dvinskikh, S. Artamonov, V. Piskunova, Inexact relative smoothness and strong convexity for optimization and variational inequalities by inexact model, Preprint no. 2709, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2709 .
Abstract, PDF (463 kByte)
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, Bregman proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal conditional gradient method and universal method for variational inequalities with composite structure. These method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. As a particular case of our general framework, we introduce relative smoothness for operators and propose an algorithm for VIs with such operator. We also generalize our framework for relatively strongly convex objectives and strongly monotone variational inequalities.

D. Gahururu, M. Hintermüller, S.-M. Stengl, Th.M. Surowiec, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion, Preprint no. 2654, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2654 .
Abstract, PDF (337 kByte)
PDE-constrained (generalized) Nash equilibrium problems (GNEPs) are considered in a deterministic setting as well as under uncertainty. This includes a study of deterministic GNEPs with nonlinear and/or multivalued operator equations as forward problems and PDE-constrained GNEPs with uncertain data. The deterministic nonlinear problems are analyzed using the theory of generalized convexity for set-valued operators, and a variational approximation approach is proposed. The stochastic setting includes a detailed overview of the recently developed theory and algorithms for risk-averse PDE-constrained optimization problems. These new results open the way to a rigorous study of stochastic PDE-constrained GNEPs.

M. Ebeling-Rump, D. Hömberg, R. Lasarzik, Th. Petzold, Topology optimization subject to additive manufacturing constraints, Preprint no. 2629, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2629 .
Abstract, PDF (1099 kByte)
In Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem.

M.H. Farshbaf Shaker, M. Gugat, H. Heitsch, R. Henrion, Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints, Preprint no. 2626, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2626 .
Abstract, PDF (424 kByte)
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented.

C. Grässle, M. Hintermüller, M. Hinze, T. Keil, Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities, Preprint no. 2617, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2617 .
Abstract, PDF (11 MByte)
We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn--Hilliard Navier--Stokes system involving a nonsmooth energy potential.We establish the existence of optimal solutions and present two distinct approaches to derive suitable stationarity conditions for the bilevel problem, namely C- and strong stationarity. Moreover, we demonstrate the numerical realization of these concepts at the hands of two adaptive solution algorithms relying on a specifically developed goal-oriented error estimator.In addition, we present a model order reduction approach using proper orthogonal decomposition (POD-MOR) in order to replace high-fidelity models by low order surrogates. In particular, we combine POD with space-adapted snapshots and address the challenges which are the consideration of snapshots with different spatial resolutions and the conservation of a solenoidal property.

F. Auricchio, E. Bonetti, M. Carraturo, D. Hömberg, A. Reali, E. Rocca, Structural multiscale topology optimization with stress constraint for additive manufacturing, Preprint no. 2615, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2615 .
Abstract, PDF (2815 kByte)
In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer.

M. Hintermüller, T. Keil, Optimal control of geometric partial differential equations, Preprint no. 2612, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2612 .
Abstract, PDF (15 MByte)
Optimal control problems for geometric (evolutionary) partial differential inclusions are considered. The focus is on problems which, in addition to the nonlinearity due to geometric evolution, contain optimization theoretic challenges because of non-smoothness. The latter might stem from energies containing non-smooth constituents such as obstacle-type potentials or terms modeling, e.g., pinning phenomena in microfluidics. Several techniques to remedy the resulting constraint degeneracy when deriving stationarity conditions are presented. A particular focus is on Yosida-type mollifications approximating the original degenerate problem by a sequence of nondegenerate nonconvex optimal control problems. This technique is also the starting point for the development of numerical solution schemes. In this context, also dual-weighted residual based error estimates are addressed to facilitate an adaptive mesh refinement. Concerning the underlying state model, sharp and diffuse interface formulations are discussed. While the former always allows for accurately tracing interfacial motion, the latter model may be dictated by the underlying physical phenomenon, where near the interface mixed phases may exist, but it may also be used as an approximate model for (sharp) interface motion. In view of the latter, (sharp interface) limits of diffuse interface models are addressed. For the sake of presentation, this exposition confines itself to phase field type diffuse interface models and, moreover, develops the optimal control of either of the two interface models along model applications. More precisely, electro-wetting on dielectric is used in the sharp interface context, and the control of multiphase fluids involving spinodal decomposition highlights the phase field technique. Mathematically, the former leads to a Hele-Shaw flow with geometric boundary conditions involving a complementarity system due to contact line pinning, and the latter gives rise to a Cahn-Hilliard Navier-Stokes model including a non-smooth obstacle type potential leading to a variational inequality constraint.

A. Alphonse, M. Hintermüller, C.N. Rautenberg, Stability of the solution set of quasi-variational inequalities and optimal control, Preprint no. 2582, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2582 .
Abstract, PDF (321 kByte)
For a class of quasivariational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve an objective with set-valued arguments. The approach to study the solution stability is based on perturbations of minimal and maximal elements to the solution set of the QVI with respect to monotonic perturbations of the forcing term. It is shown that different assumptions are required for studying decreasing and increasing perturbations and that the optimization problem of interest is well-posed.

M. Hintermüller, Functional-analytic and numerical issues in splitting methods for total variation-based image reconstruction, The Fifth International Conference on Numerical Analysis and Optimization, January 6 - 9, 2020, Sultan Qaboos University, Oman, January 6, 2020.

M. Hintermüller, Magnetic resonance fingerprinting of integrated physics models, Efficient Algorithms in Data Science, Learning and Computational Physics, January 12 - 16, 2020, Sanya, China, January 15, 2020.

K. Papafitsoros, Automatic distributed regularization parameter selection in Total Generalized Variation image reconstruction via bilevel optimization, Seminar, Shenzhen MSU-BIT University, Department of Mathematics, Shenzhen, China, January 16, 2020.

K. Papafitsoros, Automatic distributed regularization parameter selection in imaging via bilevel optimization, Workshop on PDE Constrained Optimization under Uncertainty and Mean Field Games, January 28 - 30, 2020, WIAS, Berlin, January 30, 2020.

K. Papafitsoros, Spatially dependent parameter selection in TGV based image restoration via bilevel optimization, Efficient Algorithms in Data Science, Learning and Computational Physics, Sanya, China, January 12 - 16, 2020.

A. Alphonse, Directional differentiability for elliptic quasi-variational inequalities, Workshop ``Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, Stochastic, Non-local and Discrete Structures'', January 20 - 26, 2019, Mathematisches Forschungsinstitut Oberwolfach, January 25, 2019.

A. Alphonse, Directional differentiability for elliptic quasi-variational inequalities, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Best Paper Session, August 5 - 8, 2019, Berlin, August 5, 2019.

H. Heitsch, Optimal Neumann boundary control of the vibrating string with uncertain initial data and probabilistic terminal constraints, The XV International Conference on Stochastic Programming (ICSP XV), Minisymposium ``Nonlinear Programming with Probability Functions'', July 29 - August 2, 2019, Norwegian University of Science and Technology, Trondheim, Norway, July 30, 2019.

T. Keil, Optimal control of a coupled Cahn--Hilliard--Navier--Stokes system with variable fluid densities, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Session ``Optimal Control of Phase Field Models'', August 5 - 8, 2019, Berlin, August 5, 2019.

S.-M. Stengl, M. Hintermüller, On the convexity of optimal control problems involving nonlinear PDEs or VIs, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Berlin, August 5 - 8, 2019.

S.-M. Stengl, On the convexity of optimal control problems involving nonlinear PDEs or VIs, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Session ``Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems (Part I)'', August 5 - 8, 2019, Berlin, August 6, 2019.

C. Löbhard, Space-time discretization for parabolic optimal control problems with state constraints, ICCOPT 2019 -- Sixth International Conference on Continuos Optimization, Session ``Optimal Control and Dynamical Systems (Part VI)'', August 5 - 8, 2019, Berlin, August 7, 2019.

R. Sandilya, Error bounds for discontinuous finite volume discretisa-tions of Brinkman optimal control problems, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Session ``Quasi-Variational Inequalities and Generalized Nash Equi-librium Problems (Part II)'', August 5 - 8, 2019, Berlin, August 7, 2019.

M. Ebeling-Rump, Topology optimization subject to additive manufacturing constraints, INdAM Workshop MACH2019 ``Mathematical Modeling and Analysis of Degradation and Restoration in Cultural Heritage'', March 25 - 29, 2019, Istituto Nazionale di Alta Matematica ``Francesco Severi'', Rome, Italy, March 26, 2019.

M. Ebeling-Rump, Topology optimization subject to additive manufacturing constraints, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Session ``Infinite-Dimensional Optimization of Nonlinear Systems (Part III)'', August 5 - 8, 2019, Berlin, August 6, 2019.

R. Henrion, Nonsmoothness in the context of probability functions, Workshop 4 within the Special Semester on Optimization ``Nonsmooth Optimization'', November 25 - 27, 2019, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 25, 2019.

R. Henrion, On some extended models of chance constraints, Workshop ``Mathematical Optimization of Systems Impacted by Rare, High-Impact Random Events'', June 24 - 28, 2019, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, USA, June 24, 2019.

R. Henrion, Optimal Neumann boundary control of the vibrating string under random initial conditions, OVA9: 9th International Seminar on Optimization and Variational Analysis, Universidad Miguel Hernández, Elche, Spain, September 2, 2019.

R. Henrion, Optimal Neumann boundary control of the vibrating string with uncertain initial data, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, Session ``PDE-constrained Optimization under Uncertainty (Part I)'', August 5 - 8, 2019, Berlin, August 8, 2019.

R. Henrion, Optimal probabilistic control of the vibrating string under random initial conditions, PGMO DAYS 2018, Session 1E ``Stochastic Optimal Control'', December 3 - 4, 2019, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF'Lab Paris-Saclay, Palaiseau, France, December 4, 2019.

R. Henrion, Probabilistic constraints in optimization with PDEs, Workshop 3 within the Special Semester on Optimization ``Optimization and Inversion under Uncertainty'', November 11 - 15, 2019, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 13, 2019.

R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Spring School in Nonsmooth Analysis and Optimization, April 16 - 18, 2019, Université Mohammed V, Rabat, Morocco.

R. Henrion, Robust control of a sweeping process with probabilistic end-point constraints, The XV International Conference on Stochastic Programming (ICSP XV), Minisymposium ``Nonlinear Programming with Probability Functions'', July 29 - August 2, 2019, Norwegian University of Science and Technology, Trondheim, Norway, July 30, 2019.

M. Hintermüller, Generalized Nash equilibrium problems with PDEs connected to spot markets with (gas) transport, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Session MS ME-1-4 1 ``Recent Advances in PDE-constrained Optimization'', July 15 - 19, 2019, Valencia, Spain, July 15, 2019.

M. Hintermüller, Generalized Nash equilibrium problems with application to spot markets with gas transport, Workshop ``Electricity Systems of the Future: Incentives, Regulation and Analysis for Efficient Investment'', March 18 - 22, 2019, Isaac Newton Institute, Cambridge, UK, March 21, 2019.

M. Hintermüller, Generalized Nash games with PDEs and applications in energy markets, French-German-Swiss Conference on Optimization (FGS'2019), September 17 - 20, 2019, Nice, France, September 20, 2019.

M. Hintermüller, Lecture Series: Optimal control of nonsmooth structures, Thematic Programme ``Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions'', February 4 - 7, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Colloquium of the Mathematical Institute, University of Oxford, UK, June 7, 2019.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland, December 3, 2019.

M. Hintermüller, Optimal control problems involving nonsmooth structures, Autumn School 2019 ``Optimal Control and Optimization with PDEs'' (ALOP), October 7 - 10, 2019, Universität Trier.

R. Lasarzik, Optimal control via relative energies, Workshop ``Recent Trends in Optimal Control of Partial Differential Equations'', February 25 - 27, 2019, Technische Universität Berlin, February 27, 2019.

R. Lasarzik, Weak entropic solutions to a model in induction hardening: Existence and weak-strong uniqueness, Decima Giornata di Studio Università di Pavia -- Politecnico di Milano Equazioni Differenziali e Calcolo delle Variazioni, Politecnico di Milano, Italy, February 21, 2019.

R. Lasarzik, Weak entropy solutions in the context of induction hardening, 9th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium CP FT-1-7 9 ``Partial Differential Equations VII'', July 15 - 19, 2019, Valencia, Spain, July 19, 2019.

C.N. Rautenberg, A nonlocal variational model in image processing associated to the spatially variable fractional Laplacian, ICCOPT 2019 -- Sixth International Conference on Continuous Optimization, August 5 - 8, 2019, Berlin, August 6, 2019.

C.N. Rautenberg, Parabolic quasi-variational inequalities with gradient and obstacle type constraints, Thematic Programme ``Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions'', January 28 - February 1, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, January 31, 2019.

N. Alia, Modeling and optimization of a gas-stirred liquid flow for steelmaking processes, The 20th European Conference on Mathematics for Industry (ECMI), MS27: MSO for steel production and manufacturing, June 18 - 22, 2018, University Budapest, Institute of Mathematics at Eötvös Loránd, Hungary, June 19, 2018.

A. Alphonse, Optimal Control of Elliptic and Parabolic Quasi-Variational Inequalities, Annual Meeting of the DFG Priority Programme 1962, October 1 - 3, 2018, Kremmen (Sommerfeld), October 3, 2018.

A. Alphonse, Parabolic quasi-variational inequalities: Existence and sensitivity analysis, 4th Central European Set-Valued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, Philipps-Universität Marburg, November 24, 2018.

A. Alphonse, Directional differentiability for elliptic QVIs of obstacle type, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19 - 23, 2018, Technische Universität München, March 20, 2018.

A. Alphonse, Directional differentiability for elliptic quasi-variational inequalities, Workshop ``Challenges in Optimal Control of Nonlinear PDE-Systems'', April 8 - 14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 12, 2018.

M.J. Arenas Jaén, Modelling, simulation and optimization of inductive pre-heating for thermal cutting of steel plates, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18 - 22, 2018, Budapest, Hungary, June 19, 2018.

L. Capone, Induction hardening of cam profiles: Modeling, simulation, and optimization, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18 - 22, 2018, Budapest, Hungary, June 19, 2018.

T. Keil, Simulation and Control of a Nonsmooth Cahn--Hilliard--Navier--Stokes System with Variable Fluid Densities, Annual Meeting of the DFG Priority Programme 1962, October 1 - 3, 2018, Kremmen (Sommerfeld), Germany, October 2, 2018.

T. Keil, Strong stationarity conditions for the optimal control of a Cahn--Hilliard--Navier--Stokes system, 5th European Conference on Computational Optimization, Session ``Infinite Dimensional Nonsmooth Optimization'', September 10 - 12, 2018, Trier, September 12, 2018.

S.-M. Stengl, Generalized Nash equilibrium problems with partial differential operators: theory, algorithms and risk aversion, Annual Meeting of the DFG Priority Programme 1962, October 1 - 3, 2018, Kremmen (Sommerfeld), October 1, 2018.

C. Löbhard, Analysis, algorithms and applications for the optimal control of variational inequalities, European Women in Mathematics (EWM) General Meeting 2018, Minisymposium 9 ``Nonsmooth PDE-constrained Optimization: Problems and Methods'', September 3 - 7, 2018, Karl-Franzens-Universität Graz, Austria, September 7, 2018.

C. Löbhard, Optimal shape design of air ducts in combustion engines, ROMSOC Mid--Term Meeting, November 26 - 27, 2018, Universität Bremen, November 26, 2018.

P. Dvurechensky, Computational optimal transport: Accelerated gradient descent vs Sinkhorn, ISMP 2018 Bordeaux, July 1 - 6, 2018, University of Bordeaux, Institut de Mathématiques, France, July 4, 2018.

P. Dvurechensky, Computational optimal transport: Accelerated gradient descent vs. Sinkhorn's algorithm, Statistical Optimal Transport, July 24 - 25, 2018, Skolkovo Institute of Science and Technology, Moscow, Russian Federation, July 25, 2018.

P. Dvurechensky, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, The 35th International Conference on Machine Learning (ICML 2018), Stockholm, Sweden, July 9 - 15, 2018.

P. Dvurechensky, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, The 35th International Conference on Machine Learning (ICML 2018), July 9 - 15, 2018, International Machine Learning Society (IMLS), Stockholm, Sweden, July 11, 2018.

P. Dvurechensky, Faster algorithms for (regularized) optimal transport, Grenoble Optimization Days 2018, June 28 - 29, 2018, Université Grenoble Alpes, Laboratoire Jean Kuntzmann, France, June 29, 2018.

P. Dvurechensky, Primal-dual methods for solving infinite-dimensional games, Games, Dynamics and Optimization GDO2018, March 13 - 15, 2018, Universität Wien, Fakultät für Mathematik, Austria, March 15, 2018.

R. Henrion, Dynamic chance constraints under continuous random distribution, PGMO DAYS 2018, Session 1E ``Stochastic Optimization'', November 20 - 21, 2018, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF'Lab Paris-Saclay, Palaiseau, France, November 21, 2018.

R. Henrion, Lipschitz properties and their moduli for constraint mappings, 4th Central European Set-Valued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, Philipps-Universität Marburg, November 24, 2018.

R. Henrion, M-stationary conditions for MPECs in finite dimension (Part 1+2), SPP 1962 Summer School on Complementarity Problems in Applied Mathematics: Modeling, Analysis, and Optimization, July 30 - August 1, 2018, Technische Universität Dortmund, July 31, 2018.

R. Henrion, Optimization problems under probabilistic constraints, 3rd Russian-German Conference on MultiScale BioMathematics: Coherent Modeling of Human Body System, November 7 - 9, 2018, Lomonosov Moscow State University, Russian Federation, November 8, 2018.

R. Henrion, Perspectives in probabilistic programming under continuous random distributions, Workshop ``New Directions in Stochastic Optimisation'', August 19 - 25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 20, 2018.

R. Henrion, Verification and comparison of the calmness of generalized equations in original and enhanced form, International Workshop on Optimization and Variational Analysis, January 10 - 11, 2018, Termas de Cauquenes, Chile, January 11, 2018.

M. Hintermüller, Automated regularization parameter choice rule in image processing, Workshop ``New Directions in Stochastic Optimisation'', August 19 - 25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 23, 2018.

M. Hintermüller, Bilevel optimization and some "parameter learning" applications in image processing, SIAM Conference on Imaging Science, Minisymposium MS5 ``Learning and Adaptive Approaches in Image Processing'', June 5 - 8, 2018, Bologna, Italy, June 5, 2018.

M. Hintermüller, Generalised Nash equilibrium problems with partial differential equations, Search Based Model Engineering Workshop, August 7 - 9, 2018, King's College London, UK, August 7, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, International Workshop on PDE-Constrained Optimization, Optimal Controls and Applications, December 10 - 14, 2018, Sanya, China, December 13, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, 23rd International Symposium on Mathematical Programming (ISMP2018), July 1 - 6, 2018, Bordeaux, France, July 2, 2018.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Mathematisches Kolloquium, Universität Bielefeld, Fakultät für Mathematik, June 7, 2018.

M. Hintermüller, Recent advances in non-smooth and complementarity-based distributed parameter systems, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19 - 23, 2018, Technische Universität München, March 20, 2018.

M. Hintermüller, Semismooth Newton methods in PDE constrained optimization, Advanced Training in Mathematics Schools ``New Directions in PDE Constrained Optimisation'', March 12 - 16, 2018, National Centre for Mathematics of IIT Bombay and TIFR, Mumbai, Bombay, India.

R. Lasarzik, Generalized solution concepts to the Ericksen--Leslie equations modeling liquid crystal flow, 28th IFIP TC 7 Conference on System Modelling and Optimization, July 23 - 27, 2018, Universität Duisburg-Essen, Essen, July 26, 2018.

C.N. Rautenberg, On the optimal control of quasi-variational inequalities, 23rd International Symposium on Mathematical Programming (ISMP2018), Session 221 ``Optimization Methods for PDE Constrained Problems'', July 1 - 6, 2018, Bordeaux, France, July 3, 2018.

C.N. Rautenberg, Optimization problems with quasi-variational inequality constraints, Workshop ``Challenges in Optimal Control of Nonlinear PDE-Systems'', April 8 - 14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 11, 2018.

C.N. Rautenberg, Spatially distributed parameter selection in Total Variation (TV) models, MIA 2018 -- Mathematics and Image Analysis, Humboldt-Universität zu Berlin, January 15 - 17, 2018.

C.N. Rautenberg, Evolutionary quasi-variational inequalities: Applications, theory, and numerics, 5th International Conference on Applied Mathematics, Design and Control: Mathematical Methods and Modeling in Engineering and Life Sciences, November 7 - 9, 2018, San Martin National University, Buenos Aires, Argentina, November 9, 2018.

A. Alphonse, Optimal control of elliptic and parabolic quasi-variational inequalities, Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 10, 2017.

T. Keil, Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities (with Carmen Graessle), Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 11, 2017.

T. Keil, Strong stationarity conditions for the optimal control of a Cahn--Hilliard--Navier--Stokes system, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9 - 14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

S.-M. Stengl, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms and risk aversion (with Deborah Gahururu), Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 9, 2017.

J. Sprekels, Optimal control of PDEs: From basic principles to hard applications, International School ``Frontiers in Partial Differential Equations and Solvers'', May 22 - 25, 2017, University of Pavia, Department of Mathematics, Italy.

C. Löbhard, A function space based solution method with space-time adaptivity for parabolic optimal control problems with state constraints, PGMO Days 2017, November 13 - 14, 2017, EDF Lab Paris Saclay, France, November 14, 2017.

C. Löbhard, An adaptive space-time discretization for parabolic optimal control problem with state constraints, Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations, WIAS, Berlin, June 22, 2017.

C. Löbhard, An ddaptive discontinuous Galerkin method for a parabolic optimal control problem with state constraints . . ., Workshop on Optimization of Infinite Dimensional Non-Smooth Distributed Parameter Systems, October 4 - 6, 2017, Darmstadt, October 4, 2017.

C. Löbhard, Space-time discretization of a parabolic optimal control problem with state constraints, 18th French-German-Italian Conference on Optimization, September 25 - 28, 2017, Paderborn, September 26, 2017.

P. Dvurechensky, Adaptive similar triangles method: A stable alternative to Sinkhorn's algorithm for regularized optimal transport, Co-Evolution of Nature and Society Modelling, Problems & Experience. Devoted to Academician Nikita Moiseev centenary (Moiseev-100)., November 7 - 10, 2017, Russian Academy of Science, Federal Research Center Computer Science and Control, Moskau, Russian Federation, November 9, 2017.

P. Dvurechensky, Faster algorithms for optimal transport, 3. International Matheon Conference on Compressed Sensing and its Applications 2017, Berlin, December 4 - 8, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, Optimization and Statistical Learning, Les Houches, France, April 10 - 14, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 17 - 19, 2017.

P. Dvurechensky, Gradient method with inexact oracle for composite non-convex optimization, 18th French - German - Italian Conference on Optimization, September 25 - 28, 2017, Universität Paderborn, Fakultät für Elektrotechnik, Informatik und Mathematik, Paderborn, September 27, 2017.

P. Dvurechensky, Gradient method with inexact oracle for non convex optimization, 3rd Applied Mathematics Symposium Münster: Shape, Imaging and Optimization, February 28 - March 3, 2017.

R. Henrion, A friendly tour through the world of calmness, 11th International Conference on Parametric Optimization and Related Topics (ParaoptXI), September 19 - 22, 2017, Prague, Czech Republic, September 19, 2017.

R. Henrion, Comparing and verifying calmness conditions for MPECs, Second Workshop on Metric Bounds and Transversality (WoMBaT 2017), November 30 - December 2, 2017, RMIT University, Melbourne, Australia, November 30, 2017.

R. Henrion, Contraintes en probabilité: Formules du gradient et applications, Workshop ``MAS-MODE 2017'', Institut Henri Poincaré, Paris, France, January 9, 2017.

R. Henrion, On M-stationary condition for a simple electricity spot market model, Workshop ``Variational Analysis and Applications for Modelling of Energy Exchange'', May 4 - 5, 2017, Université Perpignan, France, May 4, 2017.

R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Université de Bourgogne, Département de Mathématiques, Dijon, France, October 25, 2017.

M. Hintermüller, (Pre)Dualization, dense embeddings of convex sets, and applications in image processing, CIM-WIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6 - 8, 2017, International Center for Mathematics, University of Lisbon, Portugal, December 6, 2017.

M. Hintermüller, (Pre)Dualization, dense embeddings of convex sets, and applications in image processing, HCM Workshop: Nonsmooth Optimization and its Applications, May 15 - 19, 2017, Hausdorff Center for Mathematics, Bonn, May 15, 2017.

M. Hintermüller, Adaptive finite element solvers for MPECs in function space, SIAM Conference on Optimization, Minisymposium MS122 ``Recent Trends in PDE-Constrained Optimization'', May 22 - 25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

M. Hintermüller, Bilevel optimization and applications in imaging, Workshop ``Emerging Developments in Interfaces and Free Boundaries'', January 22 - 28, 2017, Mathematisches Forschungsinstitut Oberwolfach.

M. Hintermüller, Bilevel optimization and applications in imaging, Mathematisches Kolloquium, Universität Wien, Austria, January 18, 2017.

M. Hintermüller, Bilevel optimization and some ``parameter learning'' applications in image processing, LMS Workshop ``Variational Methods Meet Machine Learning'', September 18, 2017, University of Cambridge, Centre for Mathematical Sciences, UK, September 18, 2017.

M. Hintermüller, Generalized Nash equilibrium problems in Banach spaces: Theory, Nikaido--Isoda-based path-following methods, and applications, The Third International Conference on Engineering and Computational Mathematics (ECM2017), Stream 3 ``Computational Optimization'', May 31 - June 2, 2017, The Hong Kong Polytechnic University, China, June 2, 2017.

M. Hintermüller, Generalized Nash games with partial differential equations, Kolloquium Arbeitsgruppe Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, June 20, 2017.

M. Hintermüller, Non-smooth structures in PDE-constrained optimization, Mathematisches Kolloquium, Universität Duisburg-Essen, Fakultät für Mathematik, Essen, January 11, 2017.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Optimization Seminar, Chinese Academy of Sciences, State Key Laboratory of Scientific and Engineering Computing, Beijing, China, June 6, 2017.

M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, Seminar, Isaac Newton Institute, Programme ``Variational Methods and Effective Algorithms for Imaging and Vision'', Cambridge, UK, August 30, 2017.

M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, University College London, Centre for Inverse Problems, UK, October 27, 2017.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Kolloquium, Friedrich-Alexander-Universität Erlangen-Nürnberg, Department Mathematik, Erlangen, May 2, 2017.

M. Hintermüller, Optimal control of multiphase fluids based on non smooth models, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9 - 14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

M. Hintermüller, Optimal control of nonsmooth phase-field models, DFG-AIMS Workshop on ``Shape Optimization, Homogenization and Control'', March 13 - 16, 2017, Mbour, Senegal, March 14, 2017.

M. Hintermüller, Recent trends in PDE-constrained optimization with non-smooth structures, Fourth Conference on Numerical Analysis and Optimization (NAOIV-2017), January 2 - 5, 2017, Sultan Qaboos University, Muscat, Oman, January 4, 2017.

M. Hintermüller, Total variation diminishing Runge--Kutta methods for the optimal control of conservation laws: Stability and order-conditions, SIAM Conference on Optimization, Minisymposium MS111 ``Optimization with Balance Laws on Graphs'', May 22 - 25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

D. Hömberg, European collaboration in industrial and applied mathematics, 25th Conference on Applied and Industrial Mathematics (CAIM), September 14 - 17, 2017, University of Iaşi, Romania, September 14, 2017.

D. Hömberg, From dilatometer experiments to distortion compensation -- Optimal control problems related to solid-solid phase transitions, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway, November 3, 2017.

D. Hömberg, MSO for steel production and manufacturing, Workshop ``Future and Emerging Mathematical Technologies in Europe'', December 11 - 15, 2017, Lorentz Center, Leiden, Netherlands, December 11, 2017.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, The 15th Annual Meeting of the China Society for Industrial and Applied Mathematics, Embedded Meeting EM02 ``A3 Workshop on Modeling and Computation of Applied Inverse Problems'', October 12 - 15, 2017, Qingdao, China, October 14, 2017.

J. Neumann, The phase field approach for topology optimization under uncertainties, ZIB Computational Medicine and Numerical Mathematics Seminar, Konrad-Zuse-Zentrum für Informationstechnik Berlin, August 25, 2016.

TH. Petzold, The MIMESIS project -- An example for an interdisciplinary research project, Leibniz-Kolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9 - 11, 2016, Leibniz-Gemeinschaft, Berlin, November 9, 2016.

P. Dvurechensky, Accelerated primal-dual gradient method for composite optimization with unknown smoothness parameter, VIII Moscow International Conference on Operations Research (ORM2016), November 18 - 21, 2016, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation, October 19, 2016.

P. Dvurechensky, Accelerated primal-dual gradient method for linearly constrained minimization Problems, VII International Conference Optimization and Applications, September 25 - 28, 2016, Montenegrin Academy of Sciences and Arts, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Sciences, University of Evora, Portugal, Moscow Institute of Physics and Technology, Russiate of Physics and Technology, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Science, Petrovac, Montenegro, September 26, 2016.

M.H. Farshbaf Shaker, A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 21, 2016.

M.H. Farshbaf Shaker, Allen--Cahn MPECs, WIAS-PGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10 - 12, 2016, WIAS Berlin, May 11, 2016.

S.P. Frigeri, On some nonlocal diffuse-interface models for binary fluids: Regularity results and applications, Congress of the Italian Society of Industrial and Applied Mathematics (SIMAI 2016), September 13 - 16, 2016, Politecnico di Milano, Italy, September 14, 2016.

S.P. Frigeri, Optimal distributed control for nonlocal Cahn--Hilliard/Navier--Stokes systems in 2D, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 24, 2016.

R. Henrion, Aspects of nondifferentiability for probability functions, 7th International Seminar on Optimization and Variational Analysis, June 1 - 3, 2016, Universidad de Alicante, Spain, June 2, 2016.

R. Henrion, Aspects of nonsmoothness for Gaussian probability functions, PGMO Days 2016 -- Gaspard Monge Program for Optimization and Operations Research, November 8 - 9, 2016, Electricité de France, Palaiseau, France, November 9, 2016.

R. Henrion, Calmness of the perturbation mappings for MPECs in original and enhanced form, International Conference on Bilevel Optimization and Related Topics, May 4 - 6, 2016, Dresden, May 6, 2016.

M. Hintermüller, S. Hajian, N. Strogies, Subproject B02 -- Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Annual Meeting of the Collaborative Research Center/Transregio (TRR) 154 ``Mathematical Modeling, Simulation and Optimization Using the Example of Gas Networks'', Technische Universität Berlin, October 4 - 5, 2016.

M. Hintermüller, S. Hajian, N. Strogies, Subproject B02 -- Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Conference ``Mathematics of Gas Transport'', Konrad-Zuse-Zentrum für Informationstechnik Berlin, October 6 - 7, 2016.

M. Hintermüller, Adaptive finite elements in total variation based image denoising, SIAM Conference on Imaging Science, Minisymposium ``Leveraging Ideas from Imaging Science in PDE-constrained Optimization'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

M. Hintermüller, Bilevel optimization for a generalized total-variation model, SIAM Conference on Imaging Science, Minisymposium ``Non-Convex Regularization Methods in Image Restoration'', May 23 - 26, 2016, Albuquerque, USA, May 26, 2016.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, 66th Workshop ``Advances in Convex Analysis and Optimization'', July 5 - 10, 2016, International Centre for Scientific Culture ``E. Majorana'', School of Mathematics ``G. Stampacchia'', Erice, Italy, July 9, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, WIAS-PGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10 - 12, 2016, WIAS Berlin, May 11, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, The Fifth International Conference on Continuous Optimization, Session: ``Recent Developments in PDE-constrained Optimization I'', August 6 - 11, 2016, Tokyo, Japan, August 10, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, June 9, 2016.

M. Hintermüller, Optimal selection of the regularisation function in a localised TV model, SIAM Conference on Imaging Science, Minisymposium ``Analysis and Parameterisation of Derivative Based Regularisation'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

M. Hintermüller, Recent trends in optimal control problems with nonsmooth structures, Computational Methods for Control of Infinite-dimensional Systems, March 14 - 18, 2016, Institute for Mathematics and its Applications, Minneapolis, USA, March 14, 2016.

M. Hintermüller, Towards sharp stationarity conditions for classes of optimal control problems for variational inequalities of the second kind, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 20, 2016.

D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

D. Hömberg, Math for steel production and manufacturing, MACSI10 -- Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8 - 9, 2016, University of Limerick, Ireland, December 9, 2016.

M. Eigel, Reliable averaging for the primal variable in the courant FEM and hierarchical error estimators on red-refined meshes, 28th Chemnitz FEM Symposium 2015, September 28 - 30, 2015, Burgstädt, September 29, 2015.

CH. Heinemann, Solvability of differential inclusions describing damage processes and applications to optimal control problems, Universität Essen-Duisburg, Fakultät für Mathematik, Essen, December 3, 2015.

D. Peschka, Mathematical modeling, analysis, and optimization of strained germanium-microbridges, sc Matheon Center Days, April 20 - 21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

J. Sprekels, Optimal boundary control problems for Cahn--Hilliard systems with dynamic boundary conditions, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 20, 2015.

M.H. Farshbaf Shaker, Introduction into optimal control of partial differential equations, May 14 - 18, 2015, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of).

M.H. Farshbaf Shaker, Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach, University of Tokyo, Graduate School of Mathematical Sciences, Japan, October 6, 2015.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 13, 2015.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, Technische Universität Berlin, Institut für Mathematik, February 5, 2015.

CH. Heinemann, Well-posedness of strong solutions for a damage model in 2D, Universitá di Brescia, Department DICATAM -- Section of Mathematics, Italy, March 13, 2015.

R. Henrion, (Sub-) Gradient formulae for probability functions with Gaussian distribution, PGMO Days 2015 -- Gaspard Monge Program for Optimization and Operations Research, October 27 - 28, 2015, ENSTA ParisTech, Palaiseau, France, October 28, 2015.

R. Henrion, (Sub-)Gradient formulae for probability functions with applications to power management, Universidad de Chile, Centro de Modelamiento Matemático, Santiago de Chile, Chile, November 25, 2015.

R. Henrion, Calmness as a constraint qualification for MPECs, International Conference on Variational Analysis, Optimization and Quantitative Finance in Honor of Terry Rockafellar's 80th Birthday, May 18 - 22, 2015, Université de Limoges, France, May 21, 2015.

R. Henrion, Conditioning of linear-quadratic two-stage stochastic optimization problems, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic, March 26, 2015.

R. Henrion, On some relations between probability functions and variational analysis, International Workshop ``Variational Analysis and Applications'', August 28 - September 5, 2015, Erice, Italy, August 31, 2015.

D. Hömberg, A crash course on optimal control, Fudan University, School of Mathematical Sciences, Shanghai, China, March 18, 2015.

D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

D. Hömberg, The digital factory -- A perspective for a closer cooperation between math and industry, Workshop ``Mathematics and Computer Science in Practice: Potential and Reality'', December 9 - 11, 2015, Prague, Czech Republic, December 9, 2015.

J. Sprekels, Optimal boundary control problems for Cahn--Hilliard systems with singular potentials and dynamic boundary conditions, Romanian Academy, Simeon Stoilow Institute of Mathematics, Bucharest, March 18, 2015.

N. Togobytska, Optimal control approach for production of multiphase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

M. Eigel, Guaranteed a posteriori error control with adaptive stochastic Galerkin FEM, SIAM Conference on Uncertainty Quantification (UQ14), March 31 - April 3, 2014, Savannah, USA, April 1, 2014.

TH. Petzold, Modellierung, Simulation und Optimierung in angewandter Mathematik am Weierstraß-Institut, Innovation Days 2014, December 1 - 2, 2014, München, December 2, 2014.

K. Sturm, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 2, 2014.

M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles, Conference on Partial Differential Equations, May 28 - 31, 2014, Novacella, Italy, May 29, 2014.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, SADCO-WIAS Young Researcher Workshop, January 29 - 31, 2014, WIAS, January 31, 2014.

R. Henrion, Calmness as a constraint qualification for MPECs, German Polish Conference on Optimization Methods and Applications, February 28 - March 4, 2014, Wittenberg, March 1, 2014.

R. Henrion, Calmness as a constraint qualification for MPECs, 6th Seminar on Optimization and Variational Analysis, University of Elche, Spain, June 3, 2014.

R. Henrion, Conditioning of linear-quadratic two-stage stochastic optimization problems, 5th Conference on Optimization Theory and its Applications (ALEL 2014), June 5 - 7, 2014, Universidad de Sevilla, Spain, June 6, 2014.

R. Henrion, Nichtlineare Optimierung bei unsicheren Nebenbedingungen, 1. Arbeitstreffen zur Initiative ``Biokybernetik'', November 20 - 21, 2014, Großkarlbach, November 20, 2014.

D. Hömberg, Modelling and simulation of multi-frequency induction hardening, Ecole Polytechnique, Laboratoire de Mécanique des Solides, Palaiseau, France, March 13, 2014.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, October 21, 2014.

D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

D. Hömberg, Multifrequency induction hardening --- Modelling, analysis, and simulation, Fudan University, School of Mathematical Sciences, Shanghai, China, March 4, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25 - 28, 2014, University of Warwick, UK, March 26, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

D. Hömberg, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

J. Sprekels, Introduction into the optimal control of PDEs, SADCO-WIAS Young Researcher Workshop, January 29 - 31, 2014, WIAS, January 31, 2014.

CH. Landry, Collision detection between robots moving along specified paths, Universität der Bundeswehr München, Institut für Mathematik und Rechneranwendung, Neubiberg, May 15, 2013.

CH. Landry, Optimizing work cells in automotive industry, Mathematics for Industry and Society, July 4 - 5, 2013, French Embassy, Berlin, July 5, 2013.

CH. Landry, Task assignment, sequencing and path-planning in robotic welding cells, 18th International Conference on Methods and Models in Automation and Robotics, August 26 - 29, 2013, Miedzyzdroje, Poland, August 27, 2013.

M. Eigel, Advances in adaptive stochastic Galerkin FEM, Workshop ``Partial Differential Equations with Random Coefficients'', November 13 - 15, 2013, WIAS, Berlin, November 14, 2013.

M. Eigel, On tensor approximations with adaptive stochastic Galerkin FEM, Eidgenössische Technische Hochschule Zürich, Seminar für Angewandte Mathematik, Switzerland, September 25, 2013.

M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, The Fourth International Conference on Continuous Optimization (ICCOPT), July 27 - August 1, 2013, Universidade Nova de Lisboa, Lisbon, Portugal, July 31, 2013.

R. Henrion, Dual stationarity conditions for MPECs, CIMPA-UNESCO-MESR-MINECO-INDIA Research School ``Generalized Nash Equilibrium Problems, Bilevel Programming and MPES'', November 25 - December 6, 2013, University of Delhi, India.

R. Henrion, Optimierungsprobleme mit Wahrscheinlichkeitsrestriktionen, Technische Universität Darmstadt, Fachbereich Mathematik, September 16, 2013.

R. Henrion, Optimization problems with probabilistic constraints, Workshop ``Numerical Methods for PDE Constrained Optimization with Uncertain Data'', January 27 - February 2, 2013, Mathematisches Forschungsinstitut Oberwolfach, January 30, 2013.

R. Henrion, Optimization problems with probabilistic constraints, Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 8, 2013.

R. Henrion, Optimization problems with probabilistic constraints, March 19 - 21, 2013, University of Ostrava, Department of Mathematics, Czech Republic.

R. Henrion, Problèmes d'optimisation avec des contraintes en probabilité, Electricité de France, Clamart, France, June 20, 2013.

R. Henrion, Stochastic optimization with probabilistic constraints, International Conference on Stochastic Programming (SP XIII), July 8 - 12, 2013, Bergamo, Italy, July 9, 2013.

R. Henrion, Optimisation sous contraintes en probabilité, Journées annuelles 2013 du Groupe de Recherche MOA, June 17 - 19, 2013, Paris, France, June 17, 2013.

D. Hömberg, An optimal shape design approach towards distortion compensation, Equadiff13, MS21 -- Recent Trends in PDE-constrained Control and Shape Design, August 26 - 30, 2013, Prague, Czech Republic, August 29, 2013.

D. Hömberg, An optimal shape design approach towards distortion compensation, Fudan University, School of Mathematics, Shanghai, China, March 6, 2013.

D. Hömberg, Mathematics for the digital factory, Mathematics for Industry and Society, July 4 - 5, 2013, French Embassy, Berlin, July 5, 2013.

D. Hömberg, MeFreSim --- Modellierung, Simulation und Optimierung des Mehrfrequenzverfahrens für die induktive Wärmebehandlung als Bestandteil der modernen Fertigung, BMBF Status Seminar ``Mathematik für Innovationen in Industrie und Dienstleistung'', June 20 - 21, 2013, Bonn, June 21, 2013.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Forum Math-for-Industry 2013 ``The Impact of Applications on Mathematics'', November 4 - 8, 2013, Kyushu University, Fukuoka, Japan, November 7, 2013.

D. Hömberg, On a phase field approach to shape optimization, Université de Paris-Sud, Laboratoire de Mathématiques, Equipe Analyse Numérique et EDP, France, January 16, 2013.

D. Hömberg, Sufficient optimality conditions for a semi-linear parabolic system, University of Tokyo, Graduate School of Mathematical Sciences, Japan, February 27, 2013.

J. Sprekels, Optimal control of Allen--Cahn equations with singular potentials and dynamic boundary conditions, DIMO2013 -- Diffuse Interface Models, September 10 - 13, 2013, Levico Terme, Italy, September 11, 2013.

J. Sprekels, Optimal control of the Allen--Cahn equation with dynamic boundary condition and double obstacle potentials: A ``deep quench'' approach, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 17, 2013.

CH. Landry, An optimal control problem for the collision-free motion planning of industrial robots, École Polytechnique Fédérale de Lausanne, Mathematics Institute of Computational Science and Engineering (MATHICSE), Switzerland, November 28, 2012.

CH. Landry, Collision-free path planning of welding robots, The 17th European Conference on Mathematics for Industry 2012 (ECMI 2012), July 23 - 27, 2012, Lund, Sweden, July 24, 2012.

CH. Landry, Modeling of the optimal trajectory of industrial robots in the presence of obstacles, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 22, 2012.

K. Sturm, Shape optimization for an interface problem in linear elasticity for distortion compensation, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 20, 2012.

R. Henrion, On (co-)derivatives of the solution map to a class of generalized equations, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 23, 2012.

R. Henrion, On the coderivative of normal cone mappings to moving sets, 58th Course ``Variational Analysis and Applications'', May 14 - 22, 2012, International School of Mathematics ``Guido Stampacchia'', Erice, Italy, May 18, 2012.

D. Hömberg, On a phase field approach to topology optimization, Mini-Workshop ``Geometries, Shapes and Topologies in PDE-based Applications'', November 25 - December 1, 2012, Mathematisches Forschungsinstitut Oberwolfach, November 27, 2012.

D. Hömberg, On the phase field approach to shape and topology optimization, University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 6, 2012.

D. Hömberg, Optimal control of multifrequency induction hardening, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17 - 21, 2012, Cortona, Italy, September 18, 2012.

D. Hömberg, Optimal control of multiphase steel production, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 23, 2012.

J. Sprekels, A time discretization for a nonstandard viscous Cahn--Hilliard system, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17 - 21, 2012, Cortona, Italy, September 19, 2012.

J. Sprekels, Optimal control problems arising in the industrial growth of bulk semiconductor single crystals, 21st International Symposium on Mathematical Programming (ISMP), Invited Session ``Optimization Applications in Industry I'', August 19 - 24, 2012, Technische Universität Berlin, August 21, 2012.

J. Sprekels, Optimal control problems arising in the industrial growth of bulk single semiconductor crystals, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 11, 2012.

CH. Landry, A minimum time control problem for finding robot motion planning, Optimization 2011, July 24 - 27, 2011, Lisbon, Portugal, July 25, 2011.

TH. Arnold, On Born approximation for the scattering by rough surfaces, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 15, 2011.

A. Möller, Capacity planning in energy networks by probabilistic programming, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 14, 2011.

R. Henrion, Progress and challenges in chance-constrained programming, SIGOPT --- International Conference on Optimization 2011, June 15 - 17, 2011, Pfalz-Akademie Lambrecht, June 15, 2011.

D. Hömberg, Mathematical concepts in steel manufacturing, Fudan University, School of Mathematics, Shanghai, China, March 29, 2011.

D. Hömberg, Optimal boundary coefficient control for parabolic equations, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20 - 23, 2011, Gargnano (Brescia), Italy, June 20, 2011.

D. Hömberg, Optimal control problems in thermomechanics, Schwerpunktskolloquium ``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, January 20, 2011.

D. Hömberg, Solid-solid phase transitions: From surface hardening of steel to laser thermo-therapy, Southeast University, Department of Mathematics, Nanjing, China, March 28, 2011.

J. Sprekels, A non-standard phase-field system of Cahn--Hilliard type for diffusive phase segregation, Schwerpunktkolloquium``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, July 14, 2011.

J. Sprekels, A nonstandard phase field system of Cahn--Hilliard type for diffusive phase segregation, Seminario Matematico e Fisico di Milano, Università degli Studi di Milano, Dipartimento di Matematica, Italy, September 21, 2011.

R. Henrion, On calmness conditions in convex bilevel programming, SIAM Conference on Optimization, May 16 - 19, 2011, Darmstadt, May 16, 2011.

R. Henrion, On joint linear probabilistic constraints with Gaussian coefficient matrix, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 14, 2011.

R. Henrion, Structure, stability and algorithmic issues of optimization problems with probabilistic constraints, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 16, 2011.

D. Hömberg, Modelling, simulation and control of multiphase steel production, International Congress on Modelling and Simulation (MODSIM 2011), December 12 - 16, 2011, Perth, Australia, December 15, 2011.

D. Hömberg, On the phase field approach to shape and topology optimization, Università degli Studi di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, November 15, 2011.

K. Krumbiegel, Optimal control approach for production of modern multiphase steels, International Congress on Industrial and Applied Mathematics (ICIAM), July 18 - 22, 2011, Vancouver, Canada, July 18, 2011.

K. Krumbiegel, Superconvergence properties for semilinear elliptic boundary control problems, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 15, 2011.

J. Sprekels, Well-posedness, asymptotic behavior and optimal control of a nonstandard phase field model for diffusive phase segregation, Workshop on Optimal Control of Partial Differential Equations, November 28 - December 1, 2011, Wasserschloss Klaffenbach, Chemnitz, November 30, 2011.

N. Togobytska, An inverse problem for laser-induced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23 - 24, 2010, September 24, 2010.

R. Henrion, Chance-constrained problems, Pre-Conference PhD Workshop, 12th Conference on Stochastic Programming (SPXII), Halifax, Canada, August 15, 2010.

R. Henrion, On a dynamic model for chance constrained programming, 12th Conference on Stochastic Programming (SPXII), August 16 - 20, 2010, Halifax, Canada, August 17, 2010.

R. Henrion, Optimization problems with probabilistic constraints, 3rd International Conference on Continuous Optimization (ICCOPT), July 26 - 29, 2010, Santiago de Chile, July 27, 2010.

D. Hömberg, A brief introduction to PDE-constrained control, Warsaw Seminar on Industrial Mathematics (WSIM'10), March 18 - 19, 2010, Warsaw University of Technology, Poland, March 18, 2010.

D. Hömberg, Steel manufacturing --- A challenge for applied mathematics, Universität Duisburg-Essen, Fachbereich Mathematik, May 11, 2010.

D. Hömberg, The mathematics of distortion, ``Seminario Matematico e Fisico di Milano'', Università degli Studi di Milano, Dipartimento di Matematica, Italy, March 1, 2010.

K. Krumbiegel, Numerical analysis for elliptic Neumann boundary control problems with pointwise state and control constraints, Technische Universität Dresden, Institut für Numerische Mathematik, May 11, 2010.

K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, May 18, 2010.

K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Summer School ``Optimal Control of Partial Differential Equations'', July 12 - 17, 2010, Cortona, Italy, July 16, 2010.

K. Krumbiegel, Sufficient optimality conditions for the Moreau--Yosida type regularization concept applied to state constrained problems, Gemeinsame Jahrestagung Deutsche Mathematiker-Vereinigung (DMV) und Gesellschaft für Didaktik der Mathematik (GDM), March 8 - 12, 2010, Ludwig-Maximilians-Universität München, March 10, 2010.

K. Krumbiegel, Sufficient optimality conditions for the Moreau-Yosida type regularization concept applied to state constrained problems, 81th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2010), March 22 - 26, 2010, Universität Karlsruhe, March 25, 2010.

J. Sprekels, Introduction to Optimal Control Problems for PDEs (mini-course), Summer School ``Optimal Control of Partial Differential Equations'', July 12 - 17, 2010, Cortona, Italy.

R. Henrion, A model for dynamic chance constraints in water reservoir management, 23rd European Conference on Operational Research (EURO23), July 6 - 8, 2009, Bonn, July 7, 2009.

R. Henrion, Answers and questions in selected topics of probabilistic programming, International Colloquium on Stochastic Modeling and Optimization, November 30 - December 1, 2009, Rutgers University, New Brunswick, USA, November 30, 2009.

R. Henrion, On stationarity conditions for an equilibrium problem with equilibrium constraints from an electricity spot market model, 23rd European Conference on Operational Research (EURO23), July 6 - 8, 2009, Bonn, July 7, 2009.

D. Hömberg, Die Wärmebehandlung von Stahl --- Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multi-phase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9 - 11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

D. Hömberg, Distortion compensation --- An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27 - 31, 2009, Buenos Aires, Argentina, July 27, 2009.

D. Hömberg, Optimal control of heat treatments and stability of milling processes --- Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

K. Krumbiegel, Optimalsteuerung mit Zustandsbeschränkungen, Universität Leipzig, Fakultät für Mathematik und Informatik, October 6, 2009.

W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26 - 28, 2008.

R. Henrion, Distance to uncontrollability for convex processes, SIGOPT International Conference on Optimization, February 18 - 21, 2008, Lambrecht, February 19, 2008.

R. Henrion, On a dynamical model for chance constrained programming, Conference on Optimization & Practices in Industry (COPI08), November 26 - 28, 2008, Clamart, France, November 28, 2008.

R. Henrion, On calculating the normal cone to a finite union of convex polyhedra, World Congress of Nonlinear Analysts (WCNA 2008), July 2 - 9, 2008, Orlando, USA, July 3, 2008.

D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

D. Hömberg, Solid-solid phase transitions --- Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

D. Hömberg, The heat treatment of steel --- A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17 - 19, 2008, Bremen, September 19, 2008.

R. Henrion, Avoidance of random obstacles by means of probabilistic constraints, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 16, 2007.

R. Henrion, Chance-constrained stochastic programming, Spring School on Stochastic Programming: Theory and Applications, University of Bergamo, Italy, April 12, 2007.

R. Henrion, Contraintes en probabilité: synthèse bibliographique et approche à la situation dynamique, Electricité de France R&D, Clamart, France, November 28, 2007.

R. Henrion, Distance to uncontrollability for convex processes, International Congress ``Mathematical Methods in Economics and Industry'' (MMEI 2007), June 3--7, Herlany, Slovakia, June 5, 2007.

R. Henrion, Eventual convexity and related properties of probabilistic constraints, 11th Conference on Stochastic Programming (SPXI), August 27 - 31, 2007, Vienna, Austria, August 31, 2007.

D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

D. Hömberg, A short course on PDE-constrained optimal control, March 20 - 30, 2007, Universitá degli Studi di Milano, Dipartimento di Matematica, Italy.

D. Hömberg, Mathematical tools for the simulation and control of heat treatments, Delphi, Puerto Real, Spain, January 16, 2007.

D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part I), University of Tokyo, Department of Mathematical Sciences, Japan, February 21, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part II), University of Tokyo, Department of Mathematical Sciences, Japan, February 22, 2007.

D. Hömberg, Thermomechanical phase transition models --- analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

R. Henrion, Initiation aux contraintes en probabilité, Electricité de France R&D, Clamart, France, May 17, 2006.

R. Henrion, On chance constraints with random coefficient matrix, 19th International Symposium on Mathematical Programming (ISMP 2006), Rio de Janeiro, Brazil, August 3, 2006.

R. Henrion, Quelques propriétés structurelles de contraintes en probabilité, Ecole Nationale des Ponts et Chaussées, Marne-la-Vallée, France, May 16, 2006.

R. Henrion, Structural analysis for some basic types of probabilistic constraints, Prague Stochastics 2006, Czech Republic, August 25, 2006.

D. Hömberg, A crash course in Nonlinear Optimization, November 13 - 23, 2006, Escuela Politécnica Nacional, Quito, Ecuador.

D. Hömberg, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

D. Hömberg, Laser surface hardening --- modelling, simulation and optimal control, 4th Korean-German Seminar on Applied Mathematics and Physics, September 24 - October 1, 2006, Erlangen, September 26, 2006.

D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28 - 31, 2006, Miedzyzdroje, Poland, August 29, 2006.

D. Hömberg, Optimal control of laser material treatments, 21st European Conference on Operational Research (EURO XXI), July 3 - 5, 2006, Reykjavik, Iceland, July 3, 2006.

D. Hömberg, Optimal control of thermomechanical phase transitions, Workshop ``Inverse and Control Problems for PDE's'', March 13 - 17, 2006, Rome, Italy, March 13, 2006.

D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14 - 18, 2006, Föhr.

D. Hömberg, Thermomechanical models of phase transitions --- modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

R. Henrion, T. Szántai, Properties and calculation of singular normal distributions, Dagstuhl Seminar on ``Algorithms for Optimization with Incomplete Information'', Schloss Dagstuhl, January 17, 2005.

R. Henrion, Calmness of chance constraints and Lipschitz properties of the value-at-risk, 22nd IFIP TC 7 Conference on System Modeling and Optimization, July 18 - 22, 2005, Turin, Italy, July 21, 2005.

R. Henrion, On the structure of linear chance constraints with random coefficients, Conference on Optimization under Uncertainties (COUCH 2005), September 28 - 30, 2005, Heidelberg, September 29, 2005.

R. Henrion, Properties of linear probabilistic constraints, INFORMS Annual Meeting, November 13 - 16, 2005, San Francisco, USA, November 14, 2005.

R. Henrion, Stability of solutions in programs with probabilistic constraints, 10-th Workshop on Well-posedness of Optimization Problems and Related Topics, September 5 - 9, 2005, Borovets, Bulgaria, September 9, 2005.

D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7 - 12, 2005, Coimbra, Portugal, June 11, 2005.

D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24 - 26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

D. Hömberg, Die Laserhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

D. Hömberg, Laser material treatments --- modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25 - 29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

D. Hömberg, Optimal control of solid-solid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17 - 23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie --- Simulations- und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3 - 4, 2005, Frankfurt am Main, November 3, 2005.

R. Henrion, J. Outrata, Calmness of constraint systems with applications, French-German-Spanish Conference on Optimization, September 20 - 24, 2004, University of Avignon, France, September 21, 2004.

R. Henrion, (Sub-)Differentiability and Lipschitz properties of singular normal distributions, 10th International Conference on Stochastic Programming, October 8 - 15, 2004, University of Arizona, Tucson, USA, October 15, 2004.

R. Henrion, Optimization problems with probabilistic constraints, 10th International Conference on Stochastic Programming, October 8 - 15, 2004, University of Arizona, Tucson, USA, October 9, 2004.

R. Henrion, Selected aspects of structure, stability and numerics in chance-constrained optimization problems, Workshop on Optimization of Stochastic Systems, Stevens Institute of Technology, Hoboken, USA, April 30, 2004.

R. Henrion, Some results on stability, structure and numerics in programs with probabilistic constraints, Universität Zürich, Wirtschaftswissenschaftliche Fakultät, Switzerland, December 20, 2004.

R. Henrion, Sur des applications multivôques du type 'calme', Séminaire de l'Equipe ACSIOM (Analyse, Calcul Scientifique Industriel et Optimisation de Montpellier), Université Montpellier, France, November 16, 2004.

D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

D. Hömberg, The induction hardening of steel --- Modelling, analysis and optimal design of inductor coils, University of Kyoto, Department of Mathematics, Japan, October 21, 2004.

D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

O. Klein, Optimierung des Temperaturfeldes bei der Sublimationszüchtung von SiC Einkristallen, DGKK Arbeitskreis Angewandte Simulation in der Kristallzüchtung, February 5 - 6, 2004, Deutsche Gesellschaft für Kristallwachstum und Kristallzüchtung e.V., Volkach, February 5, 2004.

C. Meyer, O. Klein, P. Philip, A. Rösch, J. Sprekels, F. Tröltzsch, Optimal"-steuerung bei der Herstellung von SiC-Einkristallen, MathInside---Überall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003.

R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, 18th International Symposium on Mathematical Programming (ISMP 2003), August 18 - 22, 2003, Copenhagen, Denmark, August 18, 2003.

R. Henrion, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Charles University, Institute of Mathematics, Prague, Czech Republic, April 24, 2003.

D. Hömberg, Optimal design of inductor coils, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7 - 11, 2003, Sydney, Australia, July 10, 2003.

D. Hömberg, Surface hardening of steel --- Part I: Optimal design of inductor coils, 9th IEEE International Conference on Methods and Models in Automation and Robotics, August 25 - 28, 2003, Miedzyzdroje, Poland, August 26, 2003.

A. Ivanova, P. Dvurechensky, A. Gasnikov, Composite optimization for the resource allocation problem, Preprint no. arXiv:1810.00595, Cornell University Library, arXiv.org, 2018.
Abstract
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium.

Y. Nesterov, A. Gasnikov, S. Guminov, P. Dvurechensky, Primal-dual accelerated gradient descent with line search for convex and nonconvex optimization problems, Preprint no. arXiv:1809.05895, Cornell University Library, arXiv.org, 2018.
Abstract
In this paper a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the well-known lower bounds for both convex and non-convex objective functions, possesses primal-dual properties and can be applied in the non-euclidian set-up. As far as we know this is the first such method possessing all of the above properties at the same time. We demonstrate how in practice one can efficiently use the combination of line-search and primal-duality by considering a convex optimization problem with a simple structure (for example, affinely constrained).

P. Dvurechensky, A. Gasnikov, A. Kroshnin, Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm, Preprint no. arXiv:1802.04367, Cornell University Library, arXiv.org, 2018.

P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, Preprint no. arXiv:1606.08988, Cornell University Library, arXiv.org, 2016.
Abstract
In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

R. Hildebrand, Spectrahedral cones generated by rank 1 matrices, Preprint no. arXiv:1409.4781, Cornell University Library, arXiv.org, 2014.

P.J.C. Dickinson, R. Hildebrand, Considering copositivity locally, Preprint no. 4315, Optimization Online, optimization-online.org, 2014.
Abstract
Let A be an element of the copositive cone COPn. A zero u of A is a nonnegative vector whose elements sum up to one and such that uTAu = 0. The support of u is the index set supp u  f1; : : : ; ng corresponding to the nonzero entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u. Our main result is a characterization of the cone of feasible directions at A, i.e., the convex cone KA of real symmetric nn matrices B such that there exists  > 0 satisfying A + B 2 COPn. This cone is described by a set of linear inequalities on the elements of B constructed from the set of zeros of A and their supports. This characterization furnishes descriptions of the minimal face of A in COPn, and of the minimal exposed face of A in COPn, by sets of linear equalities and inequalities constructed from the set of minimal zeros of A and their supports. In particular, we can check whether A lies on an extreme ray of COPn by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sucient condition on the irreducibility of A with respect to a copositive matrix C. Here A is called irreducible with respect to C if for all  > 0 we have A ?? C 62 COPn.