Sufficient optimality conditions and duality for mathematical programming problems with equilibrium constraints

Abstract

This paper deals with the optimality and duality for a mathematical programming problem with equilibrium constraints, MPEC for short, formulated as a mathematical programming with complementarity constraints. We establish that the M-stationary condition is a sufficient optimality condition for MPEC under the assumption of pseudolinearity on the functions involved. We formulate a Mond-Weir-type dual model for MPEC and establish weak and strong duality theorems. Suitable example is given to justify the significance of these results. To the best of our knowledge, these results have not been established till now.