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A Limited-memory Optimization Method Using the Infinitely Many Times Repeated BNS Update and Conjugate Directions
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SYSNO ASEP 0497050 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A Limited-memory Optimization Method Using the Infinitely Many Times Repeated BNS Update and Conjugate Directions 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. 351, 1 May (2019), s. 14-28Poč.str. 15 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Unconstrained minimization ; Limited-memory variable metric methods ; The repeated Byrd–Nocedal–Schnabel update ; The Lyapunov matrix equation ; Global convergence ; Numerical results Vědní obor RIV BA - Obecná matematika Obor OECD Applied mathematics Způsob publikování Omezený přístup Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000468555100003 EID SCOPUS 85057130621 DOI 10.1016/j.cam.2018.10.054 Anotace To improve the performance of the limited-memory variable metric L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in Al-Baali (1999, 2002). Since the repeating process can be time consuming, the suitable extra updates need to be selected carefully. We show that for the limited-memory variable metric BNS method, matrix updating can be efficiently repeated infinitely many times under some conditions, with only a small increase of the number of arithmetic operations. The limit matrix can be written as a block BFGS update (Vlček and Lukšan, 2018), which can be obtained by solving of some low-order Lyapunov matrix equation. The resulting method can be advantageously combined with methods based on vector corrections for conjugacy, see e.g. Vlček and Lukšan (2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1016/j.cam.2018.10.054
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