Y Liu and C Storey(1992) proposed the famous LS conjugate gradient method which has good numerical results. However, the LS method has very weak convergence under the Wolfe-type line search. In this paper, we give a new descent gradient method based on the LS method. It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search. Finally, we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP⁺ method. 

Y Liu and C Storey(1992) proposed the famous LS conjugate gradient method which has good numerical results. However, the LS method has very weak convergence under the Wolfe-type line search. In this paper, we give a new descent gradient method based on the LS method. It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search. Finally, we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP+ method.