Some properties of K-convex mappings in variable ordering settings

Abstract

We consider a generalization of standard vector optimization which is called vector optimization with variable ordering structures. The problem class under consideration is characterized by a point-dependent proper cone-valued mapping: here, the concept of K-convexity of the incorporated mapping plays an important role. We present and discuss several properties of this class such as the cone of separations and the minimal variable K-convexification. The latter one refers to a general approach for generating a variable ordering mapping for which a given mapping is K-convex. Finally, this approach is applied to a particular case.

Keywords:

• Vector optimization
• variable ordering structure
• K-convexity
• cone of separations
• minimal variable K-convexification

2010 Mathematics Subject Classifications:

• 90C29
• 90C26
• 65K05

Disclosure statement

No potential conflict of interest was reported by the author(s).