Original title: Some modifications of the limited-memory variable metric optimization methods
Authors: Vlček, Jan ; Lukšan, Ladislav
Document type: Research reports
Year: 2023
Language: eng
Series: Technical Report, volume: V-1290
Abstract: Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modified to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new efficient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
Keywords: arithmetic operations reduction; global convergence; limited-memory methods; unconstrained minimization; variable metric methods; variationally derived methods
Rights: This work is protected under the Copyright Act No. 121/2000 Coll.

Institution: Institute of Computer Science AS ČR (web)
Original record: https://hdl.handle.net/11104/0338248

Permalink: http://www.nusl.cz/ntk/nusl-519915


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