Connectedness of the approximate solution sets for set optimization problems. (16th December 2022)

• Record Type: Journal Article
• Authors: Han, Yu
• Is Part Of: Optimization. Volume 71:Number 16(2022)
• Page Start: 4819
• Page End: 4834
• Publication Date: 2022-12-16
• Subjects: Set optimization problem -- approximate solution -- scalarization -- connectedness -- arcwise connectedness; 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1969393
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l -minimal approximate solutions and weak l -minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of l -minimal approximate solutions and weak l -minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak l -minimal approximate solutions for set optimization problems.