Optimality and Duality for Semi-Infinite Mathematical Programs with Equilibrium Constraints via Tangential Subdifferentials

Abstract

In this research, we consider a class of semi-infinite mathematical programs with equilibrium constraints (SIMPEC). Then, we introduce new generalized Abadie constraint qualifications and stationary conditions and derive necessary and sufficient optimality conditions for the SIMPEC by aid of the concept of the tangential subdifferentials. Further, we formulate the Mond-Weir and Wolfe type dual models for SIMPEC in a framework of tangential subdifferentials. Furthermore, we establish weak and strong duality results for each of the said models under appropriate convexity assumptions. In addition, we illustrate some results by given example.