Název: Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Autoři: Vlček, Jan ; Lukšan, Ladislav
Typ dokumentu: Příspěvky z konference
Konference/Akce: Programs and Algorithms of Numerical Mathematics /19./, Hejnice (CZ), 20180624
Rok: 2019
Jazyk: eng
Abstrakt: 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.
Klíčová slova: global convergence; limited-memory variable metric methods; numerical results; the conjugate directions; the Lyapunov matrix equation; the repeated Byrd-Nocedal-Schnabel update; unconstrained minimization
Zdrojový dokument: Programs and Algorithms of Numerical Mathematics 19, ISBN 978-80-85823-69-1

Instituce: Ústav informatiky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný na vyžádání prostřednictvím repozitáře Akademie věd.
Původní záznam: http://hdl.handle.net/11104/0296152

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-394990


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