A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization. (22nd November 2022)

• Record Type: Journal Article
• Authors: Geoffroy, Michel H.; Larrouy, James
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1848
• Page End: 1883
• Publication Date: 2022-11-22
• Subjects: Continuity of set-valued mappings -- set approach -- set optimization -- topological convergence; 54A20 -- 49J53; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2141254
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce a topology on the power set P ( Z ) of a partially ordered normed space Z from which we derive a topological convergence on P ( Z ) along with new concepts of continuity and semicontinuity for set-valued mappings. Our goal is to propose an appropriate framework to address set optimization problems involving set relations based on a cone ordering. Taking advantage of this new setting, we establish several results regarding the well-posedness of set-valued optimization problems that are consistent with the state-of-the-art.