A proximal point method for a class of monotone equilibrium problems with linear constraints

It is well known that the equilibrium problems which often arise in engineering, economics and management applications, provide a unified framework for variational inequality, complementarity problem, optimization problem, saddle point problem and fixed point problem. In this paper, a proximal point method is proposed for solving a class of monotone equilibrium problems with linear constraints (MEP). The updates of all variables of the proximal point method are given in closed form. An auxiliary equilibrium problem is introduced for MEP via its saddle point problem. Further, we present some characterizations for solution of the auxiliary equilibrium problem and fixed point of corresponding resolvent operator. Thirdly, a proximal point method for MEP is suggested by fixed point technique. The asymptotic behavior of the proposed algorithm is established under some mild assumptions. Finally, some numerical examples are reported to show the feasibility of the proposed algorithm.