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A Note on the Legendre-Fenchel Transform of Convex Composite Functions

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Nonsmooth Mechanics and Analysis

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 12))

Abstract

In this note we present a short and clear-cut proof of the formula giving the Legendre-Fenchel transform of a convex composite function g o (f1 ..., fm) in terms of the transform of g and those of the fi′s.

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References

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Author information

Authors and Affiliations

  1. Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 4, France

    Jean-Baptiste Hiriart-Urruty

Authors
  1. Jean-Baptiste Hiriart-Urruty
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Editor information

Editors and Affiliations

  1. Université Montpellier II, Montpellier, France

    P. Alart  & O. Maisonneuve  & 

  2. University of Washington, Seattle, Washington, USA

    R. T. Rockafellar

Additional information

Dedicated to J.J. Moreau on the occasion of his 80th birthday.

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© 2006 Springer Science+Business Media, Inc.

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Hiriart-Urruty, JB. (2006). A Note on the Legendre-Fenchel Transform of Convex Composite Functions. In: Alart, P., Maisonneuve, O., Rockafellar, R.T. (eds) Nonsmooth Mechanics and Analysis. Advances in Mechanics and Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29195-4_4

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