Characterization of properly optimal elements with variable ordering structures. (3rd March 2016)

• Record Type: Journal Article
• Authors: Eichfelder, Gabriele; Gerlach, Tobias
• Is Part Of: Optimization. Volume 65:Number 3(2016)
• Page Start: 571
• Page End: 588
• Publication Date: 2016-03-03
• Subjects: vector optimization -- variable ordering structure -- proper efficiency -- scalarization; 90C29 -- 90C30 -- 90C48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1040793
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In vector optimization with a variable ordering structure, the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications, it was started to develop a comprehensive theory for these vector optimization problems. Thereby, also notions of proper efficiency were generalized to variable ordering structures. In this paper, we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow complete characterizations also in the nonconvex case.