|Publication ahead of print|
|Published online||11 July 2018|
A concept of inner prederivative for set-valued mappings and its applications
LAMIA, Dept. of Mathematics, Université des Antilles, Pointe-à-Pitre,
* Corresponding author: firstname.lastname@example.org
Revised: 4 December 2017
Accepted: 15 March 2017
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.
Mathematics Subject Classification: 49J52 / 49J53
Key words: Generalized differentiation / positively homogeneous set-valued maps / linear openness / inverse mapping theorem / set-valued optimization / welfare economics
© EDP Sciences, SMAI 2018
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