Weak Slater Qualification for Nonconvex Multiobjective Semi-infinite Programming

Abstract

We consider a nonsmooth multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints, MSIP for short. First, we introduce the weak Slater constraint qualification and derive the Karush–Kuhn–Tucker types necessary and sufficient conditions for (weakly, properly) efficient solution of the considered problem. Then, we introduce a dual of Mond–Weir type and present (weak and strong) duality results for MSIP. All results are given in terms of Clarke subdifferential.