Abstract: Recently,the alternating direction method of multipliers has attracted great attention.For a class of variatio-nal inequalities,this method is efficient,when the subproblems can be solved exactly.However,the subproblems could be too difficult or impossible to be solved exactly in many practical applications.In this paper,we proposed an inexact proxi-mal point method based on proximal point method.The subproblem is simple to have a closed form solution.Instead of solving the subproblems exactly,we used the simple projection-correction method to approximate the subproblems’ real solutions.Convergence of the proposed method is proved under mild assumptions and its efficiency is also verified by some numerical experiments.

Key words: Structured variational inequality,Alternating direction method,Proximal point method,Prediction-correction method