Abstract
The main subject of this book is the study of certain classes of nonsmooth equations. An unrenounceable device for the local analysis of smooth equations is the implicit function theorem. This theorem, however, exploits the approximation properties of the derivative of a smooth function and is thus not applicable in the nonsmooth case. In order to extend this theorem to nonsmooth functions, we have to generalize the classical derivative concept to make it applicable to nonsmooth functions. This is done in the first section of this chapter, where the Bouligand derivative is introduced as a generalization of the classical Fréchet derivative. The second section we will be mainly concerned with generalizations of the classical inverse and implicit function theorems to a class of nonsmooth functions.
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© 2012 Stefan Scholtes
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Scholtes, S. (2012). Elements from Nonsmooth Analysis. In: Introduction to Piecewise Differentiable Equations. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4340-7_3
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DOI: https://doi.org/10.1007/978-1-4614-4340-7_3
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