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Interior-Point Method for Non-Linear Non-Convex Optimization
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SYSNO ASEP 0103267 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Interior-Point Method for Non-Linear Non-Convex Optimization Překlad názvu Metoda vnitřních bodů pro nelineární nekonvexní optimalizaci Tvůrce(i) Lukšan, Ladislav (UIVT-O) SAI, RID
Matonoha, Ctirad (UIVT-O) RID, SAI
Vlček, Jan (UIVT-O) SAI, RID, ORCIDZdroj.dok. Numerical Linear Algebra with Applications. - : Wiley - ISSN 1070-5325
Roč. 11, č. 5-6 (2004), s. 431-453Poč.str. 23 s. Jazyk dok. eng - angličtina Země vyd. SE - Švédsko Klíč. slova non-linear programming ; interior point methods ; indefinite systems ; indefinite preconditioners ; preconditioned conjugate gradient method ; merit functions ; algorithms ; computational experiments Vědní obor RIV BA - Obecná matematika CEP IAA1030103 GA AV ČR - Akademie věd CEZ AV0Z1030915 - UIVT-O UT WOS 000222419700003 EID SCOPUS 10044222210 DOI 10.1002/nla.354 Anotace In this paper, we propose an algorithm for solving non-linear non-convex programming problems, which is based on the interior point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric indefinite linear system. Inexact solution of this system is obtained iteratively using indefinitely preconditioned conjugate gradient method. Theorems confirming efficiency of several indefinite preconditioners are proved. Furthermore, new merit function is defined, which includes effect of possible regularization. This regularization can be used to overcome problems with near linear dependence of active constraints. The algorithm was implemented in the interactive system for universal functional optimization UFO. Results of extensive numerical experiments are reported. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2005
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