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Nonsmoothness and quasidifferentiability

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Quasidifferential Calculus

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 29))

Abstract

This paper is an introduction to the present volume. It is first shown that quasidifferentiable functions form a very distinct class of nondifferentiable functions. This and other papers in this volume demonstrate that we do not need to consider any other class of nonsmooth functions at least from the point of view of first-order approximation. The heart of quasidifferential calculus is the concept of a quasidifferential—this replaces the concept of a gradient in the smooth case and that of a subdifferential in the convex case.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Leningrad State University, Universitetskaya nab. 7/9, 199164, Leningrad, USSR

    V. F. Demyanov & L. N. Polyakova

  2. International Institute for Applied Systems Analysis, A-2361, Laxenburg, Austria

    V. F. Demyanov

  3. Institute for Social and Economic Problems, USSR Academy of Sciences, ul. Voinova 50-a, 198015, Leningrad, USSR

    A. M. Rubinov

Authors
  1. V. F. Demyanov
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  2. L. N. Polyakova
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  3. A. M. Rubinov
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Editor information

V. F. Demyanov L. C. W. Dixon

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© 1986 The Mathematical Programming Society, Inc.

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Demyanov, V.F., Polyakova, L.N., Rubinov, A.M. (1986). Nonsmoothness and quasidifferentiability. In: Demyanov, V.F., Dixon, L.C.W. (eds) Quasidifferential Calculus. Mathematical Programming Studies, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121133

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  • DOI: https://doi.org/10.1007/BFb0121133

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00928-0

  • Online ISBN: 978-3-642-00929-7

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