On Inverse Function Theorems for Set-Valued Maps

Aubin, J.-P. & Frankowska, H. (1984). On Inverse Function Theorems for Set-Valued Maps. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-84-068

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Abstract

We prove several equivalent versions of the inverse function theorem: an inverse function theorem for smooth maps on closed subsets, one for set-valued maps, a generalized implicit function theorem for set-valued maps. We provide applications to optimization theory and local controllability of differential inclusions.

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