International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 329623, 14 pages
Research Article

A Conjugate Gradient Method for Unconstrained Optimization Problems

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China

Received 5 July 2009; Revised 28 August 2009; Accepted 1 September 2009

Academic Editor: Petru Jebelean

Copyright © 2009 Gonglin Yuan. 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.


A hybrid method combining the FR conjugate gradient method and the WYL conjugate gradient method is proposed for unconstrained optimization problems. The presented method possesses the sufficient descent property under the strong Wolfe-Powell (SWP) line search rule relaxing the parameter σ<1. Under the suitable conditions, the global convergence with the SWP line search rule and the weak Wolfe-Powell (WWP) line search rule is established for nonconvex function. Numerical results show that this method is better than the FR method and the WYL method.