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Title: Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods (English)
Author: Vlček, Jan
Author: Lukšan, Ladislav
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Hejnice, June 24-29, 2018
Issue: 2018
Year:
Pages: 177-185
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Category: math
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Summary: To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. 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 [17]. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy [16]. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method. (English)
Keyword: unconstrained minimization
Keyword: limited-memory variable metric methods
Keyword: the repeated Byrd-Nocedal-Schnabel update
Keyword: the Lyapunov matrix equation
Keyword: the conjugate directions
Keyword: global convergence
Keyword: numerical results
MSC: 65F30
MSC: 65K10
DOI: 10.21136/panm.2018.19
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Date available: 2019-04-29T13:39:25Z
Last updated: 2021-05-05
Stable URL: http://hdl.handle.net/10338.dmlcz/703083
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