Original title: Application of the Infinitely Many Times Repeated BNS Update and Conjugate Directions to Limited-Memory Optimization Methods
Authors: Vlček, Jan ; Lukšan, Ladislav
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /19./, Hejnice (CZ), 20180624
Year: 2019
Language: eng
Abstract: 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.
Keywords: global convergence; limited-memory variable metric methods; numerical results; the conjugate directions; the Lyapunov matrix equation; the repeated Byrd-Nocedal-Schnabel update; unconstrained minimization
Host item entry: Programs and Algorithms of Numerical Mathematics 19, ISBN 978-80-85823-69-1

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0296152

Permalink: http://www.nusl.cz/ntk/nusl-394990


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