OPTIMALITY CONDITIONS FOR EFFICIENT SOLUTION TO THE VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS

Abstract

In this paper, by using the generalization of Ljusternik theorem, the open mapping theorem of convex process, and the convex sets separation theorem, we give the necessary conditions for the efficient solution to the constrained vector equilibrium problems without requiring that the ordering cone in the objective space has a nonempty interior and without requiring that the the convexity conditions. By the assumption of the convexity, we give the sufficient conditions for the efficient solution. As applications, we give the necessary conditions and the sufficient conditions for efficient solution to the constrained vector variational inequalities and constrained vector optimization problems.