Convergence of the minimal sets under convexity in vector optimization

We study the behaviour of the minimal sets of a sequence of convex sets An converging to a given set A. Under suitable assumptions involving only the structure of the single sets An, we obtain the lower convergence of MinAn to MinA. In a reflexive Banach space ordered by a closed convex cone with a weakly compact base, we consider a sequence of convex sets An Mosco-converging to a set A. In the more general setting of a normed linear space ordered by a closed convex based cone (without any assumptions on the compactness of the base), we consider the stronger notion of Attouch-Wets convergence of the sequence of convex sets An. We compare our theorems with existing results related to the same topic.