Vector optimization with variable domination structure : a unifying approach

Abstract

We revisit two types of constrained vector optimization problems driven by set-valued maps, where the domination structure is defined by a cone-valued map. Within the framework of variable domination structures, we demonstrate that the approaches used in the literature cover each other. This observation enables us to design unified methods for deriving necessary optimality conditions in both cases. Our results rely on key concepts such as the Extremal Principle and the inherent incompatibility between openness and efficiency, encompassing several well-known assertions in this area of research.