A modified Wei-Yao-Liu conjugate gradient method for unconstrained optimization

In this paper, we give a modified Wei-Yao-Liu conjugate gradient method (Wei et al., 2006 [18]), which will reduce to the original Wei-Yao-Liu method, and possess the sufficient descent property without any line search. Furthermore, we prove that the presented method is globally convergent for nonconvex functions with the weak Wolfe-Powell line search. In a similar way, we also extend these results to the modified Liu-Storey method. Preliminary numerical results show that the proposed methods are effective for the given test problems.