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Advances in Optimization pp 52–76Cite as

Second-Order Generalized Derivatives: Comparisons of Two Types of Epi-Derivatives

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 382))

Abstract

We review the two main concepts of generalized second-order derivative of a nonconvex function f and we relate them. Then we turn to the calculus of these derivatives in the case f is a composite function goh with g a closed proper convex function and h a twice differentiable function. Finally we clarify the way of obtaining optimality conditions for such functions which play a key role in optimization theory and in applications.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, URA 1204-CNRS, Université de Pau et des Pays de l’Adour, Avenue de l’Université, 64000, Pau, France

    Jean Paul Penot

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  1. Jean Paul Penot
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Editors and Affiliations

  1. Lehrstuhl für Mathematik VII Fakultät für Mathematik und Informatik, Universität Mannheim, Schloß, W-6800, Mannheim, Germany

    Werner Oettli

  2. Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Postfach 6980, W-7500, Karlsruhe 1, Germany

    Diethard Pallaschke

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Penot, J.P. (1992). Second-Order Generalized Derivatives: Comparisons of Two Types of Epi-Derivatives. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-51682-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55446-2

  • Online ISBN: 978-3-642-51682-5

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