Robust efficiency and well-posedness in uncertain vector optimization problems

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.