Robust efficiency and well-posedness in uncertain vector optimization problems

Abstract

In this article, we study an uncertain vector optimization problem by using the robust optimization approach. We first introduce a concept of robust efficient solution to its robust counterpart, and then we give conditions for the existence of such solutions by the virtue of Zorn's lemma. Some notions of pointwise well-posedness for the robust counterpart of the reference problem are introduced. These notions are characterized in terms of upper continuity or compactness of approximately minimal solution maps. Sufficient conditions for well-posedness properties are also provided.

Keywords:

• Uncertain vector optimization
• robust optimization
• robust counterpart
• well-posedness

AMS CLASSIFICATIONS:

• 49J55
• 49K40
• 90B50
• 90C29

Acknowledgments

The author would like to thank the Editor and anonymous Referees for their valuable remarks and suggestions that greatly helped to improve the paper.

Disclosure statement

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