On Vector Equilibrium and Vector Variational Inequality Problems

Abstract

The scalar equilibrium problem has numerous applications in Mathematical Physics, Economics and Game Theory and includes optimization and variational inequality problems. The vector equilibrium problem (VEP) is a generalization of the scalar one and it is also extensively investigated. In this work we consider relationships between VEP and other general vector problems. First we investigate ways of transforming VEP into a vector variational inequality problem under a K-space setting and obtain the relationships between monotonicity type properties of the corresponding functions. Next, we present a new gap function for VEP which allows one to reduce VEP to a vector optimization problem with single-valued function. We also consider applications of these results to vector saddle point and inverse vector optimization problems.