A New Weak Slater Constraint Qualification for Non-Smooth Multi-Objective Semi-Infinite Programming Problems

This paper addresses a non-smooth multi-objective semi-infinite programming problem that involves a feasible set defined by inequality constraints‎. ‎Our focus is on introducing a new weak Slater constraint qualification and deriving the necessary and sufficient conditions for (weakly‎, ‎properly) efficient solutions to the problem using (weak and strong) Karush-Kuhn-Tucker types‎. ‎Additionally‎, ‎we present two duals of the Mond-Weir type for the problem and provide (weak and strong) duality results for them‎. ‎All of the results are given in terms of Clarke subdifferential‎.