Characterization of the Benson Proper Efficiency and Scalarization in Nonconvex Vector Optimization

Abstract

It is the aim of this paper to present some sufficient and necessary conditions for Benson properly efficient solutions of nonconvex optimization problems via scalarization. We consider a nonconvex vector optimization problem on a real normed space, partially ordered by a pointed convex cone with a closed bounded base. We introduce a class of convex cone-monotone functions and characterize the Benson properly efficient elements as minimal points of such functions. These characterizations are presented without any convexity, cone convexlikeness or cone boundedness assumptions on the vector optimization problem.