Locating minimal sets using polyhedral cones

In this paper, we develop a theory of localization for minimal sets of a family SS of nonempty subsets of RnRn by considering polyhedral cones. To this end, we consider the first method to locate all efficient points of a nonempty set A⊂RnA⊂Rn introduced by Yu (1974) [10].

► The first method to locate efficient points of a nonempty set introduced by Yu (1974) [10] can be extend to set optimization. ► We examine set-valued optimization problems by using the set criterion. ► We study minimal sets by using polyhedral cones. ► We introduce the notion of a KK-essential set to describe the set of all dominating points of a set.