A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization

Document Type : Research Paper


1 Department of Mathematical Sciences , Ferdowsi University of Mashhad, Mashhad, Iran

2 Ferdowsi University of Mashhad


Here, we propose a practical method for solving nonsmooth convex problems by using conjugate gradient type methods. We present a modified HS conjugate gradient method, as one of the most remarkable methods to solve smooth and large-scale optimization problems. In the case that we have a nonsmooth convex problem, by way of 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.


Articles in Press, Accepted Manuscript
Available Online from 31 July 2019
  • Receive Date: 12 January 2019
  • Revise Date: 27 June 2019
  • Accept Date: 31 July 2019
  • First Publish Date: 31 July 2019