Sub-topical functions and plus-co-radiant sets. (2nd January 2016)

• Record Type: Journal Article
• Authors: Doagooei, A.R.
• Is Part Of: Optimization. Volume 65:Number 1(2016)
• Page Start: 107
• Page End: 119
• Publication Date: 2016-01-02
• Subjects: abstract convex functions -- sub-topical functions; plus-radiant sets -- plus-co-radiant sets -- non-convex separation theorems; Primary: 26A48 -- 26B25 -- Secondary: 52A07 -- 26A51; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2014.994629
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we study sub-topical functions in the framework of abstract convexity and examine the relevant properties such as support sets, polar sets and sub-differentials for these functions. Plus-radiant and plus-co-radiant sets, and their relations with sub-topical functions are studied. Applying sub-topical functions, we present some separation theorems for both plus-radiant and plus-co-radiant sets.