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Primal Interior Point Method for Minimization of Generalized Minimax Functions

SYSNO ASEP	0347293
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Primal Interior Point Method for Minimization of Generalized Minimax Functions
Author(s)	Lukšan, Ladislav (UIVT-O)_{SAI, RID} Matonoha, Ctirad (UIVT-O)_{RID, SAI} Vlček, Jan (UIVT-O)_{SAI, RID, ORCID}
Source Title	Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954 Roč. 46, č. 4 (2010), s. 697-721
Number of pages	25 s.
Language	eng - English
Country	CZ - Czech Republic
Keywords	unconstrained optimization ; large-scale optimization ; nonsmooth optimization ; generalized minimax optimization ; interior-point methods ; modified Newton methods ; variable metric methods ; global convergence ; computational experiments
Subject RIV	BA - General Mathematics
R&D Projects	GA201/09/1957 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000284562000008
EID SCOPUS	79951615907
Annotation	In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2011

Number of the records: 1