Treatment of set order relations by means of a nonlinear scalarization functional: a full characterization. (2nd October 2016)

• Record Type: Journal Article
• Authors: Köbis, Elisabeth; Köbis, Markus A.
• Is Part Of: Optimization. Volume 65:Number 10(2016)
• Page Start: 1805
• Page End: 1827
• Publication Date: 2016-10-02
• Subjects: Set optimization -- set order relations -- nonlinear scalarizing functional -- descent method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1219355
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we show how a nonlinear scalarization functional can be used in order to characterize several well-known set order relations and which thus plays a key role in set optimization. By means of this functional, we derive characterizations for minimal elements of set-valued optimization problems using a set approach. Our methods do not rely on any convexity assumptions on the considered sets. Furthermore, we develop a derivative-free descent method for set optimization problems without convexity assumptions to verify the usefulness of our results.