A concept of inner prederivative for set-valued mappings and its applications

Abstract : We introduce a class of positively homogeneous set-valued mappings, called inner prederivatives, serving as first order approximants to set-valued mappings. We prove an inverse mapping theorem involving such prederivatives and study their stability with respect to variational perturbations. Then, taking advantage of their properties we establish necessary optimality conditions for the existence of several kind of minimizers in set-valued optimization. As an application of these last results, we consider the problem of finding optimal allocations in welfare economics. Finally, to emphasize the interest of our approach, we compare the notion of inner prederivative to the related concepts of set-valued differentiation commonly used in the literature.
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ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (3), pp.1059 - 1074. 〈10.1051/cocv/2017024 〉
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https://hal.archives-ouvertes.fr/hal-01673090
Contributeur : Michel H. Geoffroy <>
Soumis le : jeudi 28 décembre 2017 - 15:04:42
Dernière modification le : jeudi 25 octobre 2018 - 13:23:45

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Michel H. Geoffroy, Yvesner Marcelin. A concept of inner prederivative for set-valued mappings and its applications. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (3), pp.1059 - 1074. 〈10.1051/cocv/2017024 〉. 〈hal-01673090〉

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