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Interior-Point Method for Non-Linear Non-Convex Optimization

SYSNO ASEP	0103267
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Interior-Point Method for Non-Linear Non-Convex Optimization
Title	Metoda vnitřních bodů pro nelineární nekonvexní optimalizaci
Author(s)	Lukšan, Ladislav (UIVT-O)_{SAI, RID} Matonoha, Ctirad (UIVT-O)_{RID, SAI} Vlček, Jan (UIVT-O)_{SAI, RID, ORCID}
Source Title	Numerical Linear Algebra with Applications. - : Wiley - ISSN 1070-5325 Roč. 11, č. 5-6 (2004), s. 431-453
Number of pages	23 s.
Language	eng - English
Country	SE - Sweden
Keywords	non-linear programming ; interior point methods ; indefinite systems ; indefinite preconditioners ; preconditioned conjugate gradient method ; merit functions ; algorithms ; computational experiments
Subject RIV	BA - General Mathematics
R&D Projects	IAA1030103 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z1030915 - UIVT-O
UT WOS	000222419700003
EID SCOPUS	10044222210
DOI	10.1002/nla.354
Annotation	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.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2005

Number of the records: 1