New second-order radial epiderivatives and applications to optimality conditions

Zhang, Xiaoyan; Wang, Qilin

RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 949-959.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.

Classification : 90C26, 90C46
Mots-clés : Set-valued optimization problems, second-order weakly composed radial epiderivatives, Benson proper efficient solutions, second-order optimality conditions

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