A systematization of convexity and quasiconvexity concepts for set-valued maps, defined by l-type and u-type preorder relations

作者：Seto Kazuki^*; Kuroiwa Daishi; Popovici Nicolae

来源：Optimization, 2018, 67(7): 1077-1094.

DOI：10.1080/02331934.2018.1454920

• Set-valued optimization
• generalized convexity
• affine perturbation

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.

• 出版日期2018