A non-monotone Hestenes-Stiefel conjugate gradient algorithm for nonsmooth convex optimization | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 15، شماره 3، خرداد 2024، صفحه 11-20 اصل مقاله (491.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.16973.1899 | ||
| نویسندگان | ||
| Ahmad Abouyee Mehrizi؛ Reza Ghanbari* | ||
| Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Nonsmooth convex optimization؛ Conjugate gradient method؛ nonmonotone line search؛ Global convergence | ||
| مراجع | ||
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