Two new conjugate gradient methods based on modified secant equations
type: Item
instance of: scholarly article
title: Two new conjugate gradient methods based on modified secant equations
zbMATH Open document ID: 1202.65071
author: Saman Babaie-Kafaki
author: Reza Ghanbari
author: Nezam Mahdavi-Amiri
published in: Journal of Computational and Applied Mathematics
publication date: 2010-05-21T00:00:00Z
review text: Two new nonlinear conjugate gradient methods for the solution of unconstrained optimization problems are presented and evaluated. They are based on the guidelines of Dai and Liao and take into account both the gradient and function values. A modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, characterizes the first method. The second method is based on the modified BFGS update proposed by Yuan. It is shown that one of the proposed methods is globally convergent for general functions and the other is globally convergent for uniformly convex functions, under proper conditions. For the enhancement of the performance of the line search procedure, a new approach for the computation of the initial steplength for initiating the procedure is obtained. A comparison of the proposed methods with the efficient conjugate gradient methods proposed by Dai and Liao and Hestenes and Stiefel is implemented and the numerical results demonstrate the efficiency of the two methods.
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5710743
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: modified secant equation
zbMATH Keywords: conjugacy condition
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: global convergence
Wikidata QID: Q57952896
describes a project that uses: SCALCG
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: j.cam.2010.01.052
OpenAlex ID: W2141102526
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DOI: 10.1016/J.CAM.2010.01.052
description: scientific article; zbMATH DE number 5710743