Alternating multi-step quasi-Newton methods for unconstrained optimization
type: Item
instance of: scholarly article
title: Alternating multi-step quasi-Newton methods for unconstrained optimization
zbMATH Open document ID: 0886.65064
DOI: 10.1016/S0377-0427(97)00075-7
author: L. A. Moghrabi
author: J. A. Ford
published in: Journal of Computational and Applied Mathematics
publication date: 1998-04-20T00:00:00Z
review text: The authors consider multistep quasi-Newton methods for unconstrained optimization. These methods were introduced in three earlier papers of the authors, where they showed how an interpolating curve in the variable-space could be used to derive an appropriate generalization of the secant equation normally employed in the construction of quasi-Newton methods. One of the most successful of these multistep methods employs the current approximation to the Hessian to determine the parametrization of the interpolating curve and, hence, the derivatives required in the generalized updating formula. However, certain approximations were found to be necessary in the process in order to reduce the level of computation required (which must be repeated at each iteration) to acceptable levels. In this paper, the authors show how a variant of this algorithm, which avoids the need for such approximations, may be obtained. This is accomplished by alternating, on successive iterations, a single-step and a two-step method. The results of a series of experiments, which show that the new algorithm exhibits a clear improvement in numerical performance, are reported.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 1084092
zbMATH Keywords: numerical examples
zbMATH Keywords: multistep quasi-Newton methods
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: algorithm
reviewed by: Jürgen Guddat
describes a project that uses: minpack
MaRDI profile type: Publication
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full work available at URL: s0377-0427(97)00075-7
OpenAlex ID: W2065028445
description: scientific article; zbMATH DE number 1084092