Abstract: In this paper, considering the mathematical programs with equilibrium constraints is difficult to meet the constrained qualification and difficult to solve, based on the dual form of standard nonlinear programming proposed by Mond and Weir, using the S-stability, we establish the Mond-Weir type duality of equilibrium constrained optimization problem, which provides a new method for solving the problem of equilibrium constraint optimization. Under the condition of Hanson-Mond generalized convexity, the weak duality, strong duality and strict inverse duality theorem are proposed by using the sublinear function, and the corresponding proofs are given. The generalization of the dual method provides a theoretical basis for studying the solution of the mathematical programs with equilibrium constraints .

Key words: mathematical programs with equilibrium constraints(MPEC), Mond-Weir type duality, stability point