A sufficient descent Liu–Storey conjugate gradient method and its global convergence

Abstract

In this paper, a modified Liu–Storey conjugate gradient method is proposed. The method can generate sufficient descent directions for non-linear unconstrained optimization problems. A global convergence result is established when the line search fulfils the strong Wolfe conditions. Moreover, the -linear convergence rate of the methods is proved. The extensive numerical results show that the proposed method is efficient for the unconstrained optimization problems in the CUTEr library.