A systematization of convexity and quasiconvexity concepts for set-valued maps,defined by l-type and u-type preorder relations |
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| Authors: | Kazuki Seto Daishi Kuroiwa Nicolae Popovici |
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| Institution: | 1. Interdisciplinary Graduate School of Science and Engineering, Shimane University , Matsue, Japan.k.seto@math.shimane-u.ac.jp;3. Major in Interdisciplinary Science and Engineering, Shimane University , Matsue, Japan.;4. Faculty of Mathematics and Computer Science, Babe?-Bolyai University , Cluj-Napoca, Romania. |
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| Abstract: | AbstractIn 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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| Keywords: | Set-valued optimization generalized convexity affine perturbation |
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