Optimality and Wolfe duality for multiobjective bectovex programming

In this paper we extend, the concept of a sublinear functional to a becto-sublinear functional and the concepts of F -convex and generalized F -convex functions to bectovex and generalized bectovex functions, respectively. Next, we introduce a primal multiobjective programming problem, and assuming the functions to be bectovex (generalized bectovex), establish sufficient conditions for efficient and properly efficient solutions of the primal. Furthermore, we introduce a Wolfe type multiobjective dual, establish the duality results relating the dual and the primal, and relate this to certain vector saddle point of a vectorvalued Lagrangian. We also show that the duality for certain multiobjective fractional program follows as a special case of the main problem.