Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems

This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values. Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient method. Finally, some numerical results are reported to show the efficiency of our algorithm.