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.
Abouyee, A., Ghanbari, R. (2019). A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization. International Journal of Nonlinear Analysis and Applications, (), -. doi: 10.22075/ijnaa.2019.16973.1899
MLA
Ahmad Abouyee; Reza Ghanbari. "A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization". International Journal of Nonlinear Analysis and Applications, , , 2019, -. doi: 10.22075/ijnaa.2019.16973.1899
HARVARD
Abouyee, A., Ghanbari, R. (2019). 'A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization', International Journal of Nonlinear Analysis and Applications, (), pp. -. doi: 10.22075/ijnaa.2019.16973.1899
VANCOUVER
Abouyee, A., Ghanbari, R. A Nonmonotone Hestenes ans Stiefel Conjugate Gradient Algorithm for Nonsmooth Convex Optimization. International Journal of Nonlinear Analysis and Applications, 2019; (): -. doi: 10.22075/ijnaa.2019.16973.1899