Two Types Of Proximal Points Algorithms For Generalized Equilibrium Problem

In recent years, equilibrium problem and variational inequalities problem have been extensively studied. Many scholars spread the two issues from different forms, this paper studies the generalized equilibrium problem and the mixed variational inequality problem.This dissertation uses alternating direction method to solve a class of gen-eralized equilibrium problem. Alternating Direction Method is one of the classic methods to solve optimization problem with separable structure, its essence is mak-ing use of the equivalence of the solutions of original problem and the augmented Lagrangian saddle point of original problem to iterate some parameters, and then find the solution to the original problem. This dissertation corrects the Lagrange multipliers to construct a new Alternating Direction Method and analyzes conver-gence and convergence rate in the non-ergodic sense of the sequence generated by the algorithm.Some paper makes use of a general inertial proximal point algorithm to solve the mixed variational inequality problem, but the convergence condition of algorithm is not easy to set some parameter value in the iterative process. Inspired by this article, this dissertation sets the parameters directly and proves that the conditions for this parameter can launch that the original convergence condition is satisfied, and analyzes the convergence rate in the sense of ergodic, and finally carries out numerical simulation.