OPTIMALITY CONDITIONS FOR GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN VECTOR SPACES

In this paper, we consider the generalized vector equilibrium problems in the setting of vector spaces. We first establish the existence of a nonempty pointed convex cone with empty topological interior but with nonempty algebraic interior in an arbitrary infinite dimensional topological vector space. Then we establish a set-valued version of Farakas's lemma in the setting of real ordered vector spaces. By using it, we give several optimality conditions for solutions of generalized vector equilibrium problems. Some examples are given to illustrate the main results of this paper.