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A conjugate directions approach to improve the limited-memory BFGS method
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SYSNO ASEP 0378976 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A conjugate directions approach to improve the limited-memory BFGS method Author(s) Vlček, Jan (UIVT-O) SAI, RID, ORCID
Lukšan, Ladislav (UIVT-O) SAI, RIDSource Title Applied Mathematics and Computation. - : Elsevier - ISSN 0096-3003
Roč. 219, č. 3 (2012), s. 800-809Number of pages 10 s. Language eng - English Country US - United States Keywords unconstrained minimization ; variable metric methods ; limited-memory methods ; the BFGS update ; conjugate directions ; numerical results 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 000310501700004 EID SCOPUS 84867333311 DOI 10.1016/j.amc.2012.06.042 Annotation Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors, utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. Global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
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