On the strong convergence of a sufficient descent Polak-Ribière-Polyak conjugate gradient method
type: Item
instance of: scholarly article
title: On the strong convergence of a sufficient descent Polak-Ribière-Polyak conjugate gradient method
zbMATH Open document ID: 1469.65108
DOI: 10.1155/2014/283215
author: M. Sun
author: Jing Liu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Recently, \textit{L. Zhang} et al. [IMA J. Numer. Anal. 26, No. 4, 629--640 (2006; Zbl 1106.65056)] proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that \(\lim\inf_{k \rightarrow \infty} \| \nabla f(x_k) \| = 0\) when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by \textit{Z.-J. Shi} and \textit{J. Shen} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 6, 1428--1441 (2007; Zbl 1120.49027)] and Zhang et al. [loc. cit.], we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that \(\lim_{k \rightarrow \infty} \| \nabla f(x_k) \| = 0\) under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 7022086
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/283215
OpenAlex ID: W2069981619
Wikidata QID: Q59037648
cites work: Q5563083
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description: scientific article; zbMATH DE number 7022086