A systematization of convexity and quasiconvexity concepts for set-valued maps, defined by l-type and u-type preorder relations. (3rd July 2018) - Seto, Kazuki; Kuroiwa, Daishi; Popovici, Nicolae
Abstract: 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.