Lower semicontinuous functionals with uniform sublevel sets. (3rd April 2017)

• Record Type: Journal Article
• Authors: Weidner, Petra
• Is Part Of: Optimization. Volume 66:Number 4(2017)
• Page Start: 491
• Page End: 505
• Publication Date: 2017-04-03
• Subjects: Separation theorems -- vector optimization -- production theory -- mathematical finance; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1279161
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, lower semicontinuous functionals with uniform sublevel sets are investigated, where the sublevel sets are linear shifts of a set in a fixed direction. The extended real-valued functionals are defined on a topological vector space. Conditions are given under which they are proper, finite-valued, continuous, convex, sublinear, strictly quasi-convex, strictly quasi-concave or monotone. We apply the functionals to the separation of not necessarily convex sets.