Secant relations versus positive definiteness in quasi-Newton methods
type: Item
instance of: scholarly article
title: Secant relations versus positive definiteness in quasi-Newton methods
zbMATH Open document ID: 0534.90068
DOI: 10.1007/BF00938401
published in: Journal of Optimization Theory and Applications
publication date: 1984-01-01T00:00:00Z
review text: The effect of using a nonsymmetric and nonpositive-definite matrix for approximation of the Hessian inverse in unconstrained optimization is investigated. To this end, a new algorithm, which may be viewed as a member of the Huang family, is derived. The proposed algorithm possesses the quadratic termination property without exact line search. It seems from the numerical results that it is not essential to use a symmetric and positive-definite matrix.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 3848977
zbMATH Keywords: quasi-Newton methods
zbMATH Keywords: nonsymmetric nonpositive-definite matrix
zbMATH Keywords: approximation of the Hessian inverse
zbMATH Keywords: unconstrained optimization
author: Ury Passy
author: Eliezer Z. Prisman
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00938401
OpenAlex ID: W2087978208
description: scientific article; zbMATH DE number 3848977