On lagrange type duality theory for nonsmooth optimization problems with equilibrium constraints

Abstract

In this paper, we consider a special class of optimization problems known as the mathematical problem with equilibrium constraints (MPEC). We formulate Lagrange type dual problems for the MPEC and establish weak and strong duality results under convexity assumptions. Further, we discuss the saddle point optimality criteria for the MPEC. An example is given to illustrate the obtained results.