Strict weak l-efficient solutions for nonconvex set optimization problems

Abstract

In this article, we introduce the notions of l-transfer lower continuous and q-level intersectionally closed for set-valued mappings with respect to the lower set less relation. Then, we obtain some existence results for strict weak l-efficient solutions of such set-valued mappings. Moreover, we prove some existence results for nonconvex set optimization problems via asymptotic analysis tools, in the setting of the Banach spaces equipped with a Hausdorff topology σ coarser than the norm topology.

Keywords:

• Set optimization problem
• transfer lower continuous
• q-level intersectionally closed
• asymptotic analysis

Acknowledgments

The authors would like to thank the reviewers for their constructive comments, which helped us to improve the paper.

Disclosure statement

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

Additional information

Funding

The fourth author was partially supported by a grant from IPM [grant number 1401460421].