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Generalizations of the limited-memory BFGS method based on the quasi-product form of update
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SYSNO ASEP 0381640 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Generalizations of the limited-memory BFGS method based on the quasi-product form of update Tvůrce(i) Vlček, Jan (UIVT-O) SAI, RID, ORCID
Lukšan, Ladislav (UIVT-O) SAI, RIDZdroj.dok. Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 241, 15 March (2013), s. 116-129Poč.str. 14 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova unconstrained minimization ; variable metric methods ; limited-memory methods ; Broyden class updates ; global convergence ; numerical results Vědní obor RIV BA - Obecná matematika CEP GA201/09/1957 GA ČR - Grantová agentura ČR CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000312354100008 EID SCOPUS 84868223108 DOI https://doi.org/10.1016/j.cam.2012.09.027 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2013
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