Connectedness of the approximate solution sets for set optimization problems

ABSTRACT

In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak l-minimal approximate solutions for set optimization problems.

KEYWORDS:

• Set optimization problem
• approximate solution
• scalarization
• connectedness
• arcwise connectedness

AMS SUBJECT CLASSIFICATIONS:

• 49J53
• 90C29

Acknowledgements

The author is grateful to the reviewers for their valuable comments and suggestions.

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 [grant number 11801257].