The interior proximal extragradient method for solving equilibrium problems |
| |
Authors: | Thi Thu Van Nguyen Jean-Jacques Strodiot Van Hien Nguyen |
| |
Institution: | (1) Department of Mathematics, University of Namur (FUNDP), Namur, Belgium;(2) Faculty of Mathematics and Informatics, University of Natural Sciences, Vietnam National University, Ho Chi Minh City, Vietnam |
| |
Abstract: | In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on
an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type
algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a
first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm
the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that
our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for
the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms. |
| |
Keywords: | Interior proximal method Logarithmic-quadratic proximal method Extragradient method Armijo-backtracking linesearch Equilibrium problems |
本文献已被 SpringerLink 等数据库收录! |