Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ

Christian Grossmann; Diethard Klatte; Bernd Kummer

Kybernetika (2004)

  • Volume: 40, Issue: 5, page [571]-584
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Grossmann, Christian, Klatte, Diethard, and Kummer, Bernd. "Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ." Kybernetika 40.5 (2004): [571]-584. <http://eudml.org/doc/33720>.

@article{Grossmann2004,
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.},
author = {Grossmann, Christian, Klatte, Diethard, Kummer, Bernd},
journal = {Kybernetika},
keywords = {log-barrier method; Mangasarian–Fromovitz constraint qualification; convergence ofprimal-dual solutions; locally linearized problems; Lipschitz estimates; log-barrier method; Mangasarian-Fromovitz constraint qualification; convergence of primal-dual solutions; linear independence constraint qualification (LICQ); Mangasarian-Fromovitz constraint qualification (MFCQ)},
language = {eng},
number = {5},
pages = {[571]-584},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ},
url = {http://eudml.org/doc/33720},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Grossmann, Christian
AU - Klatte, Diethard
AU - Kummer, Bernd
TI - Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 5
SP - [571]
EP - 584
AB - 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.
LA - eng
KW - log-barrier method; Mangasarian–Fromovitz constraint qualification; convergence ofprimal-dual solutions; locally linearized problems; Lipschitz estimates; log-barrier method; Mangasarian-Fromovitz constraint qualification; convergence of primal-dual solutions; linear independence constraint qualification (LICQ); Mangasarian-Fromovitz constraint qualification (MFCQ)
UR - http://eudml.org/doc/33720
ER -

References

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