Studies On Duality For A Class Of Mathematical Programs With Equilibrium Constraints

This paper considers duality in mathematical programs with complementarity con-straints(MPCC). Based on duality for nonlinear programming, we present Wolfe-type and Mond-Weir-type duality for mathematical programs with complementary constraints, and the corresponding duality theorems.The main content is organized as following:1. Based on Wolfe duality for nonlinear programming, we present a Wolfe-type duality for MPCC and establish the weak duality theorem, the direct duality theorem, the strict converse duality theorem and the strict converse duality theorem under some suitable conditions. In particular, we show that a linear MPCC is equivalent to a linear programming problem in some sense. Then, we use examples to illustrate that Wolfe duality for mathematical programs with complementarity constraints is sensible.2. On the basis of the Wolfe duality for mathematical programs with complementary con-straints, convexity conditions are weakened into a pseudo-convex, pseudoconvex conditions, we consider the Mond-Weir type duality in mathematical programs with complementarity con-straints(MPCC), and give the weak duality theorem, the strong duality theorem and the strict converse duality theorem. Then, we use examples to illustrate that Mond-Weir duality for math-ematical programs with complementarity constraints is sensible.