Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

Abstract In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient are proved for such nonconvex smooth vector optimization problems. Further, duals in sense Mond–Weir defined considered and several duality results established also hypotheses.