Semi-infinite Mathematical Programming Problems involving Generalized Convexity

Abstract

In this paper, we consider semi-infinite mathematical programming problems withequilibrium constraints (SIMPEC). By using the notion of convexificators, we establish sufficient optimality conditions for the SIMPEC. We formulate Wolfe and Mond-Weir type dual models for the SIMPEC under generalized convexity assumptions. Moreover, weak and strong duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators.