Convergence of minimal sets in convex vector optimization

We study the behavior of the minimal sets of a sequence of convex sets {A_n} converging to a given set A. The main feature of the present work is the use of convexity properties of the sets A_n and A to obtain upper and lower convergence of the minimal frontiers. We emphasize that we study both Kuratowski–Painlev´e convergence and Attouch–Wets convergence of minimal sets. Moreover, we prove stability results that hold in a normed linear space ordered by a general cone, in order to deal with the most common spaces ordered by their natural nonnegative orthants (e.g., C ([a, b]) , l_p, and L_p (R) for 1 ≤ p≤∞). We also make a comparison with the existing results related to the topics considered in our work.