Global Well-Posedness in Set Optimization

Abstract

In this paper we introduce and study two concepts of global well-posedness for set optimization problems in Hausdorff topological vector spaces. Some relationships among these notions and generalized e-well-posedness concept already existent in the literature are established. Sufficient conditions are also given in order to guarantee global well-posedness. Our notions and results extend similar concepts and results established for set optimization problems in metric spaces.

Keywords:

• Generalized convexity
• generalized e-well-posedness
• generalized M-well-posedness
• global well-posedness
• M-well-posedness
• set optimization problem
• the lower set order relation

6. Data Availability statements

Author can confirm that all relevant data are included in the article.

Acknowledgments

The author would like to express his gratitude to the anonymous referees for their helpful comments which improved the presentation of the paper.