Geodesic
Weak and Proper Efficiency in Set-Valued Optimization on Real Linear Spaces
Journal of convex analysis, Tome 14 (2007) no. 2, pp. 275-296.

Voir la notice de l'article provenant de la source Heldermann Verlag

We extend the notion of cone-subconvexlikeness of set-valued maps on topological linear spaces to set-valued maps on linear spaces, (that is, general linear spaces without any particular topology), and we provide several characterizations. An alternative theorem is also established for this kind of maps. Using the notion of vector closure introduced recently by Adán and Novo, we also provide, in this framework, an adaptation of the proper efficiency in the sense of Benson for set-valued maps. The previous notion and results are then applied to obtain optimality conditions of weak efficiency and a characterization of Benson proper efficiency by means of scalarization and multipliers rules.
Classification : 90C29, 90C46
Mots-clés : Set-valued maps, set-valued optimization, proper efficiency, generalized convexity 
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     title = {Weak and {Proper} {Efficiency} in {Set-Valued} {Optimization} on {Real} {Linear} {Spaces}},
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E. Hernández; B. Jiménez; V. Novo. Weak and Proper Efficiency in Set-Valued Optimization on Real Linear Spaces. Journal of convex analysis, Tome 14 (2007) no. 2, pp. 275-296. https://geodesic-test.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a4/