Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 463087, 22 pages
http://dx.doi.org/10.1155/2011/463087
Research Article

Global Convergence of a Nonlinear Conjugate Gradient Method

Liu Jin-kui, Zou Li-min, and Song Xiao-qian

School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, China

Received 5 March 2011; Revised 21 May 2011; Accepted 4 June 2011

Academic Editor: Piermarco Cannarsa

Copyright © 2011 Liu Jin-kui et al. 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

A modified PRP nonlinear conjugate gradient method to solve unconstrained optimization problems is proposed. The important property of the proposed method is that the sufficient descent property is guaranteed independent of any line search. By the use of the Wolfe line search, the global convergence of the proposed method is established for nonconvex minimization. Numerical results show that the proposed method is effective and promising by comparing with the VPRP, CG-DESCENT, and DL+ methods.