Set optimization by means of variable order relations

Abstract

We introduce several variable order relations to compare sets in a linear topological space and we consider set optimization problems equipped with these variable ordering structures. By considering a set approach, we introduce characterizations for optimal solutions and we provide a kind of vectorization result to obtain solutions of set optimization problems equipped with the introduced variable order relations.

Keywords:

• Set optimization
• variable ordering structures
• cone-valued map
• vectorization

Acknowledgements

The author is grateful to two anonymous referees for helpful suggestions and valuable comments.

Notes

No potential conflict of interest was reported by the author.