Optimality Conditions For Vector Equilibrium Problems When The Constraint Cone Has An Empty Interior

In this paper, first of all, we present the necessary and sufficient conditions for weakly efficient solution to the vector equilibrium problems with constraints by using the notion of quasi interior of a convex set when the constraint cone has an empty interior. As applications, we give the necessary and sufficient conditions for weakly efficient solution to the vector variational inequalities and vector optimization problems with constraints. Then, we present the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution and globally properly efficient solution to the set-valued vector equilibrium problems with constraints when the constraint cone has an empty interior. As applications, we give the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution and globally properly efficient solution to the set-valued vector variational inequalities and vector optimization problems with constraints, respectively.