The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions
type: Item
instance of: scholarly article
title: The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions
zbMATH Open document ID: 1152.65068
author: Liying Liu
author: Shengwei Yao
author: Zengxin Wei
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-22T00:00:00Z
review text: This article extends two existing papers, namely one by \textit{J. Han} and \textit{G. Liu} [Comput. Optim. Appl. 7, No.~3, 277--289 (1997; Zbl 0876.90072)] and one by \textit{Z. Wei, G. Yu, G. Yuan} and \textit{Z. Lian} [Comput. Optim. Appl. 29, No.~3, 315--332 (2004; Zbl 1070.90089)], these could have been cited properly to shorten the discussed work. As in the latter reference the authors introduce a slightly modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula (MBFGS) for the solution of unconstrained optimization problems, but instead of the more standard Wolfe-type line-search a ``GLL'' line search is used. This on the other hand has been studied with the standard BFGS formula in the primer reference. The steps to prove global convergence are taken from this paper nearly unchanged, so are the lemmas from Wei et al. [loc. cit.] for proving superlinear convergence. The paper ends with numerical comparisons on a test-set where one can see that the difference between the ``nonmonotone'' MBFGS, the Wolfe-MBFGS and also the ``nonmonotone'' standard BFGS is negligible.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 5315410
zbMATH Keywords: GLL line search
zbMATH Keywords: superlinear convergence
zbMATH Keywords: global convergence
zbMATH Keywords: quasi-Newton method
zbMATH Keywords: Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula
zbMATH Keywords: numerical examples
reviewed by: M. D. Korzec
describes a project that uses: ve08
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: j.cam.2007.08.017
OpenAlex ID: W1969738095
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DOI: 10.1016/J.CAM.2007.08.017
description: scientific article; zbMATH DE number 5315410