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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 517452, 5 pages
http://dx.doi.org/10.1155/2013/517452
Research Article

A Global Convergence of LS-CD Hybrid Conjugate Gradient Method

Department of Mathematics and Econometrics, Hunan University of Humanities, Science, and Technology, Loudi 417000, China

Received 25 June 2013; Revised 3 September 2013; Accepted 4 September 2013

Academic Editor: William J. Layton

Copyright © 2013 Xiangfei Yang 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

Conjugate gradient method is one of the most effective algorithms for solving unconstrained optimization problem. In this paper, a modified conjugate gradient method is presented and analyzed which is a hybridization of known LS and CD conjugate gradient algorithms. Under some mild conditions, the Wolfe-type line search can guarantee the global convergence of the LS-CD method. The numerical results show that the algorithm is efficient.