On M-Stationary Conditions and Duality for Multiobjective Mathematical Programs with Vanishing Constraints

Mathematical programs with vanishing constraints are the optimization problems that do not satisfy most of the constraint qualifications due to nonconvex feasible region. Hence, some weaker first-order conditions like M-stationary come into existence. In this paper, we establish necessary and sufficient M-stationary conditions for multiobjective mathematical problems with vanishing constraints. We formulate Wolfe and Mond–Weir type dual models for the treated problem and propose weak, strong and strict converse duality results for Wolfe and Mond–Wier dual models. Further, we provide some examples in the support of our theory.