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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 283215, 7 pages
http://dx.doi.org/10.1155/2014/283215
Research Article

On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

1School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, China
2School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China

Received 2 December 2013; Revised 9 January 2014; Accepted 10 January 2014; Published 23 February 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Min Sun and Jing Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recently, Zhang et al. 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 when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that 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.