A method of duality for a mixed vector equilibrium problem

Abstract

In this paper, a dual scheme for a mixed vector equilibrium problem is introduced by using the method of Fenchel conjugate function. Under the stabilization condition, the relationships between the solutions of mixed vector equilibrium problem (MVEP) and dual mixed vector equilibrium problem (DMVEP) are discussed. Moreover, under the same condition, the solutions of MVEP and DMVEP are proved relating to the saddle points of an associated Lagrangian mapping. As applications, this dual scheme is applied to vector convex optimization and vector variational inequality.