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.
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