Well-posedness and stability of solutions for set optimization problems

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.

Keywords:

• Set optimization problem
• set-valued mapping
• well-posedness
• upper semi-continuity
• lower semi-continuity

Acknowledgements

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

Notes

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 number 11171237], [grant number 11471230], [grant number 11671282]; the joint Foundation of the Ministry of Education of China and China Mobile Communication Corporation [grant number MCM20150505].