Number of the records: 1
Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
- 1.
SYSNO ASEP 0504548 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods Author(s) Vlček, Jan (UIVT-O) SAI, RID, ORCID
Lukšan, Ladislav (UIVT-O) SAI, RIDSource Title Programs and Algorithms of Numerical Mathematics 19. - Prague : Institute of Mathematics of the Czech Academy of Sciences, 2019 / Chleboun J. ; Kůs P. ; Přikryl P. ; Rozložník M. ; Segeth K. ; Šístek J. ; Vejchodský T. - ISBN 978-80-85823-69-1 Pages s. 177-185 Number of pages 9 s. Publication form Online - E Action Programs and Algorithms of Numerical Mathematics /19./ Event date 24.06.2018 - 29.06.2018 VEvent location Hejnice Country CZ - Czech Republic Event type WRD Language eng - English Country CZ - Czech Republic Keywords unconstrained minimization ; limited-memory variable metric methods ; the repeated Byrd-Nocedal-Schnabel update ; the Lyapunov matrix equation ; the conjugate directions ; global convergence ; numerical results Subject RIV BA - General Mathematics OECD category Applied mathematics Institutional support UIVT-O - RVO:67985807 UT WOS 000576737400019 DOI 10.21136/panm.2018.19 Annotation To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time. The limit update is a block BFGS update. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2020
Number of the records: 1