On Nonsmooth Multiobjective Semi-Infinite Programming Problems with Mixed Constraints

We consider the multiobjective semi-infinite programming problems with feasible sets defined by equality and inequality constraints, in which the objective and the constraints functions are locally Lipschitz. First, we introduce an Arrow-Hurwitcz-Uzawa type constraint qualification which is based on the Clarke subdifferential. Then, we derive the strong Karush-Kuhn-Tucker type necessary optimality condition for properly efficient solutions of the considered problems.