Some properties of K-convex mappings in variable ordering settings. (9th December 2022)

• Record Type: Journal Article
• Authors: Bouza Allende, Gemayqzel; Hernández Escobar, Daniel; Rückmann, Jan-J.
• Is Part Of: Optimization. Volume 71:Number 14(2022)
• Page Start: 4125
• Page End: 4146
• Publication Date: 2022-12-09
• Subjects: Vector optimization -- variable ordering structure -- K-convexity -- cone of separations -- minimal variable K-convexification; 90C29 -- 90C26 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1937159
• Languages: English
• ISSNs: 0233-1934

Abstract

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.