Necessary and Sufficient Optimality Conditions in DC Semi-infinite Programming

This paper deals with particular families of DC optimization problems involving suprema convex functions. We show that the specific structure this type function allows us to cover a variety in nonconvex programming. Necessary and sufficient optimality conditions for these are established, where some structural features conveniently exploited. More precisely, we derive necessary (global local) semi-infinite programming cone-constrained optimization, under natural constraint qualifications. Finally, penalty approach abstract is developed last section.