Weak Slater Qualification for Nonconvex Multiobjective Semi-infinite Programming

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.