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Kybernetika 40(5):571-584, 2004.

Convergence of Primal-Dual Solutions for the Nonconvex Log-Barrier Method without LICQ

C. Grossman, D. Klatte and B. Kummer


Abstract:

This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well--known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual solutions without applying additionally technical tools arising from Newton--techniques.


Keywords: log-barrier method; Mangasarian--Fromovitz constraint qualification; convergence ofprimal-dual solutions; locally linearized problems; Lipschitz estimates;


AMS: 90C30; 65K10; 49K40; 49M37;


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BIB TeX

@article{kyb:2004:5:571-584,

author = {Grossman, C. and Klatte, D. and Kummer, B.},

title = {Convergence of Primal-Dual Solutions for the Nonconvex Log-Barrier Method without LICQ},

journal = {Kybernetika},

volume = {40},

year = {2004},

number = {5},

pages = {571-584}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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