Nonconvex Separation Functional in Linear Spaces with Applications to Vector Equilibria

Abstract

In this paper, the so-called nonconvex separation functional is studied in a real linear space not necessarily endowed with a topology. The essential properties of this functional, which are well known in the topological framework, are derived by using algebraic counterparts to the topological concepts of interior and closure. Finally, it is used to characterize, in the same algebraic setting and by scalarization, weak efficient solutions of vector equilibrium problems defined through algebraic solid ordering sets.