International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 329623, 14 pages
doi:10.1155/2009/329623

A conjugate gradient method for unconstrained optimization problems

Abstract

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.