A nonmonotonic explicit proximal-like method for solving equilibrium programming with convex constraints

[摘要] In this paper, we propose a new proximal-type method to solve equilibrium problems in a real Hilbert space. The new method is analogous to the famous two step extragradient method that is used to solve variational inequalities in the Hilbert spaces. The proposed iterative scheme uses a new non-monotone step size rule based on local bifunction information instead of any line search method. A strong convergence theorem for the proposed method is well-established by taking mild conditions on a bifunction. The applications of the main results to solve fixed point problems and variational inequalities are presented. Finally, we examined two test problems for computational experiments and demonstrated the validity and effectiveness of the proposed method.

[学科分类] 公共、环境与职业健康

[关键词] Lipschitz-type condition;Equilibrium problem;Variational inequalities