An efficient conjugate gradient method with strong convergence properties for non-smooth optimization

In this paper, we introduce an efficient conjugate gradient method for solving nonsmooth optimization problems by using the Moreau-Yosida regularization approach. The search directions generated by our proposed procedure satisfy the sufficient descent property, and more importantly, belong to a suitable trust region.  Our proposed method is globally convergent under mild assumptions. Our numerical comparative results on a collection of test problems show the efficiency and superiority of our proposed method. We have also examined the ability and the effectiveness of our approach for solving some real-world engineering problems from image processing field. The results confirm better performance of our method.