Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints

The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of a vector equilibrium problem with setvalued mappings and cone constraints. Using a separation theorem which involves the quasi-relative interior of a convex set, we obtain optimality conditions for solutions of the considered vector equilibrium problem. The main theorem recovers an earlier established result. Then, the results are applied to vector optimization problems and to Stampacchia vector variational inequalities with cone constraints.

Existence Theorems for Vector Equilibrium Problems via Quasi-Relative Interior

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.

ON A SEPARATION THEOREM INVOLVING THE QUASI-RELATIVE INTERIOR

We establish two separation theorems in which the classic interior is replaced by the quasi-relative interior.