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Primal Interior Point Method for Minimization of Generalized Minimax Functions
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SYSNO ASEP 0347293 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Primal Interior Point Method for Minimization of Generalized Minimax Functions Tvůrce(i) Lukšan, Ladislav (UIVT-O) SAI, RID
Matonoha, Ctirad (UIVT-O) RID, SAI
Vlček, Jan (UIVT-O) SAI, RID, ORCIDZdroj.dok. Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 46, č. 4 (2010), s. 697-721Poč.str. 25 s. Jazyk dok. eng - angličtina Země vyd. CZ - Česká republika Klíč. slova unconstrained optimization ; large-scale optimization ; nonsmooth optimization ; generalized minimax optimization ; interior-point methods ; modified Newton methods ; variable metric methods ; global convergence ; computational experiments Vědní obor RIV BA - Obecná matematika CEP GA201/09/1957 GA ČR - Grantová agentura ČR CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000284562000008 EID SCOPUS 79951615907 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2011
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