A systematization of convexity and quasiconvexity concepts for set-valued maps, defined by l-type and u-type preorder relations. (3rd July 2018)

• Record Type: Journal Article
• Authors: Seto, Kazuki; Kuroiwa, Daishi; Popovici, Nicolae
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1077
• Page End: 1094
• Publication Date: 2018-07-03
• Subjects: Set-valued optimization -- generalized convexity -- affine perturbation; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1454920
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we study different classes of generalized convex/quasiconvex set-valued maps, defined by means of the l -type and u -type preorder relations, currently used in set-valued optimization. In particular, we identify those classes of set-valued maps for which it is possible to extend the classical characterization of convex real-valued functions by quasiconvexity of their affine perturbations.