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Journal of Convex Analysis 25 (2018), No. 2, 595--622
Copyright Heldermann Verlag 2018

Semismooth Implicit Functions

Florian Kruse
Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010 Graz, Austria

Semismoothness of implicit functions in infinite-dimensional spaces is investigated. We provide sufficient conditions for the semismoothness of given implicit functions and show how the existence of implicit functions that fulfill these conditions can be ensured. This approach also extends some finite-dimensional results.

Keywords: Semismoothness, implicit function theorems, nonsmooth analysis, superposition operators, generalized derivatives, optimal control.

MSC: 47H30, 47J07, 49J20, 49J52

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