On the stability of minimal solutions for parametric set optimization problems

Abstract

In this paper, we establish the upper semi-continuity, lower semi-continuity and compactness of relaxed minimal and minimal solution mappings for parametric set optimization problems, where the objective set-valued mappings take values in the topological space introduced by Geoffroy [A topological convergence on power sets well-suited for set optimization. J Global Optim. 2019;73:567–581].

Keywords:

• Parametric set optimization problem
• relaxed minimal solution
• minimal solution
• topological space

2010 Mathematics Subject Classifications:

• 90C29
• 90C31
• 54A20

Acknowledgments

The authors are grateful to the editor and the referees for their valuable 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 11471230, 11671282].