Journal of Applied Mathematics
Volume 2012 (2012), Article ID 641276, 13 pages
http://dx.doi.org/10.1155/2012/641276
Research Article

Global Convergence of a Modified Spectral Conjugate Gradient Method

Huabin Jiang,1 Songhai Deng,2 Xiaodong Zheng,2 and Zhong Wan2

1Department of Electronic Information Technology, Hunan Vocational College of Commerce, Hunan, Changsha 410205, China
2School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China

Received 20 September 2011; Revised 25 October 2011; Accepted 25 October 2011

Academic Editor: Giuseppe Marino

Copyright © 2012 Huabin Jiang 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 spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergence is established. Numerical results demonstrate that this algorithm is promising, particularly, compared with the existing similar ones.