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Some modiﬁcations of the limited-memory variable metric optimization methods

SYSNO ASEP	0566981
Document Type	V - Research Report
R&D Document Type	The record was not marked in the RIV
Title	Some modiﬁcations of the limited-memory variable metric optimization methods
Author(s)	Vlček, Jan (UIVT-O)_{SAI, RID, ORCID} Lukšan, Ladislav (UIVT-O)_{SAI, RID}
Issue data	Prague: ICS CAS, 2023
Series	Technical Report
Series number	V-1290
Number of pages	11 s.
Publication form	Online - E
Language	eng - English
Country	CZ - Czech Republic
Keywords	unconstrained minimization ; variable metric methods ; limited-memory methods ; variationally derived methods ; arithmetic operations reduction ; global convergence
Institutional support	UIVT-O - RVO:67985807
Annotation	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.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2023

Number of the records: 1