Lower semicontinuous functionals with uniform sublevel sets
Petra Weidner · Optimization · 2017
In this paper, lower semicontinuous functionals with uniform sublevel sets are investigated, where the sublevel sets are linear shifts of a set in a fixed direction. The extended real-valued functionals are defined on a topological vector space. Conditions are given under which they are proper, finite-valued, continuous, convex, sublinear, strictly quasi-convex, strictly quasi-concave or monotone. We apply the functionals to the separation of not necessarily convex sets.