A new algorithm of nonlinear conjugate gradient method with strong convergence
type: Item
instance of: scholarly article
title: A new algorithm of nonlinear conjugate gradient method with strong convergence
zbMATH Open document ID: 1172.90014
author: Zhenjun Shi
author: Jinhua Guo
published in: Computational and Applied Mathematics
publication date: 2008-12-11T00:00:00Z
review text: This paper considers an unconstrained minimization problem: \[ \text{min} f(x), \quad x \in\mathbb R^n \] Where \(\mathbb R^n\) is an dimensioinal Euclidean space and \(f:\mathbb R^n\to\mathbb R\) is a continuous differentiable function. If \(n\) is very large, this problem is a large scale problem. Motivated by \textit{Y.-X. Yuan} and \textit{J. Stoer}'s conjugate gradient algorithms [Z. Angew. Math. Mech. 75, No.~1, 69--77 (1995; Zbl 0823.65061)], this paper applies the trust region technique to the conjugate gradient methods. The new algorithm has both global convergence and good numerical performance in practical computation. The theoretical analysis and numerical results show that the proposal algorithm is promising and can solve ill conditional minimization problems. The new method can generate an adequate trust region radius automatically at each iteration and also has a linear convergence rate under some mild conditions. Numerical results show that the new conjugate method is superior to other simple conjugate methods in many situations.
reviewed by: Lai-Jiu Lin
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 5381831
zbMATH Keywords: unconstraint optimization
zbMATH Keywords: global convergence
zbMATH Keywords: linear convergence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5381831