Optimality and duality in multiobjective programming involving support functions

In this paper a vector optimization problem (VOP) is considered where each component of objective and constraint function involves a term containing support function of a compact convex set. Weak and strong Kuhn[Formula: see text]Tucker necessary optimality conditions for the problem are obtained under suitable constraint qualifications. Necessary and sufficient conditions are proved for a critical point to be a weak efficient or an efficient solution of the problem (VOP) assuming that the functions belong to different classes of pseudoinvex functions. Two Mond Weir type dual problems are considered for (VOP) and duality results are established.