Number of the records: 1
Generalizations of the limited-memory BFGS method based on the quasi-product form of update
- 1.
SYSNO ASEP 0381640 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Generalizations of the limited-memory BFGS method based on the quasi-product form of update Author(s) Vlček, Jan (UIVT-O) SAI, RID, ORCID
Lukšan, Ladislav (UIVT-O) SAI, RID, ORCIDSource Title Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 241, 15 March (2013), s. 116-129Number of pages 14 s. Language eng - English Country NL - Netherlands Keywords unconstrained minimization ; variable metric methods ; limited-memory methods ; Broyden class updates ; global convergence ; 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 000312354100008 EID SCOPUS 84868223108 DOI https://doi.org/10.1016/j.cam.2012.09.027 Annotation Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methods is established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
Number of the records: 1