The stability of the solution sets for set optimization problems via improvement sets. (2nd November 2019)

• Record Type: Journal Article
• Authors: Mao, Jia-yu; Wang, San-hua; Han, Yu
• Is Part Of: Optimization. Volume 68:Number 11(2019)
• Page Start: 2171
• Page End: 2193
• Publication Date: 2019-11-02
• Subjects: Parametric set optimization problem -- improvement set -- solution mapping -- lower semi-continuity -- upper semi-continuity; 49J45 -- 49J53 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1579813
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The aim of this paper is to investigate the stability of the solution sets for set optimization problems via improvement sets. Firstly, we consider the relations among the solution sets for optimization problem with set optimization criterion. Then, the closeness and the convexity of solution sets are discussed. Furthermore, the upper semi-continuity, Hausdorff upper semi-continuity and lower semi-continuity of solution mappings to parametric set optimization problems via improvement sets are established under some suitable conditions. These results extend and develop some recent works in this field.