The stability of the solution sets for set optimization problems via improvement sets

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.

KEYWORDS:

• Parametric set optimization problem
• improvement set
• solution mapping
• lower semi-continuity
• upper semi-continuity

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49J45
• 49J53
• 90C31

Acknowledgements

The authors are grateful to the editor and the referees for their useful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11661055, 11201216, 11661056, 11771198 and 11801257], the Natural Science Foundation of Jiangxi Province [grant number 20151BAB201020], the China Postdoctoral Science Foundation [grant number 2015M582047], the Postdoctoral Science Foundation of Jiangxi Province [grant number 2016KY58]; the Science Fund of the Education Department of Jiangxi Province [grant number GJJ160063].