A new scalarization approach and applications in set optimization. (3rd April 2023)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc; Thanh Duoc, Pham; Thi Thuy Duong, Tran
• Is Part Of: Optimization. Volume 72:Number 4(2023)
• Page Start: 1093
• Page End: 1117
• Publication Date: 2023-04-03
• Subjects: Set optimization problem -- set less order relation -- nonlinear scalarization -- optimality condition -- scalar representation; 49K35 -- 49M37 -- 65K05 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2023.2172983
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the power set of a normed space and discuss its properties. Next, we apply such properties to formulate sufficient and necessary optimality conditions for strictly minimal and weakly minimal sets. Finally, under suitable adjustments, we provide nonlinear scalarization functions and investigate scalar representations of strictly efficient solution and weakly efficient solution sets of the reference problems.