Characterizations of set relations with respect to variable domination structures via oriented distance function. (2nd September 2018)

• Record Type: Journal Article
• Authors: Ansari, Qamrul Hasan; Köbis, Elisabeth; Sharma, Pradeep Kumar
• Is Part Of: Optimization. Volume 67:Number 9(2018)
• Page Start: 1389
• Page End: 1407
• Publication Date: 2018-09-02
• Subjects: Oriented distance function -- set optimization -- set relations -- variable domination structures -- optimality conditions; 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1493108
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we characterize several known set relations with respect to variable domination structures by defining scalarization functions in terms of the oriented distance function. The characterization of minimal elements of a family of sets and the properties of sets of minimal elements are discussed by means of scalarization functionals. An application of variable domination structures to uncertain vector optimization is also given.