a non-monotone hestenes-stiefel conjugate gradient algorithm for nonsmooth convex optimization

Here, we propose a practical method for solving nonsmooth convex problems by using conjugate gradient-type methods. the conjugate gradient method is one of the most remarkable methods to solve smooth and large-scale optimization problems. as a result of this fact, we present a modified hs conjugate gradient method. in the case that we have a nonsmooth convex problem, by the moreau-yosida regularization, we convert the nonsmooth objective function to a smooth function and then we use our method, by making use of a nonmonotone line search, for solving a nonsmooth convex optimization problem. we prove that our algorithm converges to an optimal solution under standard condition. our algorithm inherits the performance of hs conjugate gradient method.