Geodesic
Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ
Kybernetika, Tome 40 (2004) no. 5, p. [571].

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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.
Classification : 49K40, 49M37, 65K10, 90C30
Keywords: log-barrier method; Mangasarian–Fromovitz constraint qualification; convergence ofprimal-dual solutions; locally linearized problems; Lipschitz estimates 
@article{KYB_2004__40_5_a3,
     author = {Grossmann, Christian and Klatte, Diethard and Kummer, Bernd},
     title = {Convergence of primal-dual solutions for the nonconvex log-barrier method without {LICQ}},
     journal = {Kybernetika},
     pages = {[571]},
     publisher = {mathdoc},
     volume = {40},
     number = {5},
     year = {2004},
     mrnumber = {2120997},
     zbl = {1249.90252},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a3/}
}
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Grossmann, Christian; Klatte, Diethard; Kummer, Bernd. Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ. Kybernetika, Tome 40 (2004) no. 5, p. [571]. http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a3/