Well-posedness and scalarization in vector optimization

In this paper, we study several existing notions of well-posedness
for vector optimization problems. We separate them into two
classes and we establish the hierarchical structure of their relationships.
Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well posed.