Cone enlargements and applications to vector optimization

Abstract

We study four types of enlargements for cones in normed vector spaces. We identify some commune features and mutual inclusions that these enlargements enjoy under different classical properties of cones: normality, well-basedness and so on. The effect of such conic enlargements on the behavior of the Gerstewitz (Tammer) scalarizing functional is shortly presented. Then we prove that, in the virtue of their inclusions, all these enlargements are involved in the study of the properness of several types of solutions in a variety of vector optimization problems.