On duality for mathematical programs with vanishing constraints

In this paper, we formulate and study Wolfe and Mond–Weir type dual models for a difficult class of optimization problems known as the mathematical programs with vanishing constraints. We establish the weak, strong, converse, restricted converse and strict converse duality results under the assumptions of convexity and strict convexity between the primal mathematical program with vanishing constraints and the corresponding Wolfe type dual. We also derive the weak, strong, converse, restricted converse and strict converse duality results between the primal mathematical program with vanishing constraints and the corresponding Mond–Weir type dual under the assumptions of pseudoconvex, strict pseudoconvex and quasiconvex functions.