A proximal bundle technique for solving equilibrium problems with inexact information

Abstract

In this study, we describe a bundle approach used to solve the nonsmooth equilibrium problems was described. Firstly, a general algorithm was considered, and the algorithm's validity was demonstrated by showing how it can provide a sequence that converges to an approximate solution for the equilibrium problem. Moreover, in this strategy, using the inaccurate value of the objective function and the approximate gradient of the adjacent points, a proximal bundle algorithm is created to solve equilibrium problems, and the inaccurate value makes the subproblem easy to solve and maintains convergence. So, we find a simpler way to solve the equilibrium problem.