Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Florian Kruse

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

florian.kruse@uni-graz.at

Keywords

  • Semismoothness
  • implicit function theorems
  • nonsmooth analysis
  • superposition operators
  • generalized derivatives
  • optimal control

Mathematics Subject Classification

47H30, 47J07, 49J20, 49J52

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Suggested citation

F. Kruse. “Semismooth Implicit Functions.” Journal of Convex Analysis 25 (2018), No. 2, 595–622. https://doi.org/10.68381/jca25037

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.