Painlevé–Kuratowski convergences of the solution sets for set optimization problems with cone-quasiconnectedness

ABSTRACT

This paper aims at investigating the Painlevé–Kuratowski convergence of the solution sets for set optimization problems with respect to the perturbations of the feasible set and the objective mapping. We introduce the concepts of cone-quasiconnectedness and strictly cone-quasiconnectedness for set-valued mappings and a new convergence for the sequence of set-valued mappings, and then we obtain the Painlevé–Kuratowski convergence of the sets of l-minimal solutions and weak l-minimal solutions for perturbed set optimization problems by using cone-quasiconnectedness and strictly cone-quasiconnectedness. As an application of the main results, we derive Painlevé–Kuratowski convergence of the solution sets for vector optimization problems.

Keywords:

• Set optimization problem
• Painlevé–Kuratowski convergence
• Arcwise connectedness
• cone-quasiconnectedness
• vector optimization problem

AMS Subject Classifications:

• 49J40
• 49K40
• 90C31

Acknowledgments

The author is grateful to the editor and reviewers whose helpful comments and suggestions have led to much improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11801257).