Well-posedness and stability of solutions for set optimization problems. (2nd January 2017)

• Record Type: Journal Article
• Authors: Han, Yu; Huang, Nan-jing
• Is Part Of: Optimization. Volume 66:Number 1(2017)
• Page Start: 17
• Page End: 33
• Publication Date: 2017-01-02
• Subjects: Set optimization problem -- set-valued mapping -- well-posedness -- upper semi-continuity -- lower semi-continuity; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1247270
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, some characterizations for the generalized l - B -well-posedness and the generalized u - B -well-posedness of set optimization problems are given. Moreover, the Hausdorff upper semi-continuity of l -minimal solution mapping and u -minimal solution mapping are established by assuming that the set optimization problem is l - H -well-posed and u - H -well-posed, respectively. Finally, the upper semi-continuity and the lower semi-continuity of solution mappings to parametric set optimization problems are investigated under some suitable conditions.