A systematization of convexity and quasiconvexity concepts for set-valued maps, defined byl-type andu-type preorder relations
Kazuki Seto, Daishi Kuroiwa, Nicolae Popovici · Optimization · 2018
In this paper, we study different classes of generalized convex/quasiconvex set-valued maps, defined by means of the l-type and u-type preorder relations, currently used in set-valued optimization. In particular, we identify those classes of set-valued maps for which it is possible to extend the classical characterization of convex real-valued functions by quasiconvexity of their affine perturbations.