Geodesic
A concept of inner prederivative for set-valued mappings and its applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1059-1074

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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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017024
Classification : 49J52, 49J53
Keywords: Generalized differentiation, positively homogeneous set-valued maps, linear openness, inverse mapping theorem, set-valued optimization, welfare economics

Geoffroy, Michel H. 1 ; Marcelin, Yvesner 1

1 
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     title = {A concept of inner prederivative for set-valued mappings and its applications},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1059--1074},
     publisher = {EDP-Sciences},
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     year = {2018},
     doi = {10.1051/cocv/2017024},
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     zbl = {1405.49011},
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Geoffroy, Michel H.; Marcelin, Yvesner. A concept of inner prederivative for set-valued mappings and its applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1059-1074. doi: 10.1051/cocv/2017024

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