Topological aspects in vector optimization problems

Abstract

In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive the sufficient conditions for existence of efficient solutions of the above problems and discuss the role of the topological properties of the objective space. Our main goal deals with the scalarization of vector optimization problems when the objective functions are vector-valued mappings with a weakened property of lower semicontinuity. We also prove the existence of the so-called generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.

Keywords

• vector optimization problem
• efficient solutions
• objective mapping
• property of lower semicontinuity
• generalized efficient solutions