Ahmad Abouyee Mehrizi - Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Reza Ghanbari - Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

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.

Nonsmooth convex optimization, Conjugate gradient method, nonmonotone line search, Global convergence