Abstract

This note is devoted to the clarification of the relationship between the Legendre-Fenchel conjugate of 1/f and that of -f when f is a positive concave function.

Author information

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

Jean-Baptiste Hiriart-Urruty

Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

jbhu@cict.fr

Keywords

  • Convex functions
  • Legendre-Fenchel conjugate
  • subdifferential

Mathematics Subject Classification

26B25, 52A41, 90C25

References

  1. I. Ekeland, R. Temam: Convex Analysis and Variational Problems, North Holland (1976); reprinted by SIAM (1999).https://doi.org/10.1137/1.9781611971088Google Scholar
  2. J.-B. Hiriart-Urruty, C. Lemaréchal: Convex Analysis and Minimization Algorithms, Grundlehren der Mathematischen Wissenschaften 305-306, Springer, Berlin (1993) (two volumes).https://doi.org/10.1007/978-3-662-02796-7Google Scholar
  3. J.-B. Hiriart-Urruty, J. E. Martínez-Legaz: New formulas for the Legendre-Fenchel transform, J. Math. Anal. Appl. 288(2) (2003) 544–555.https://doi.org/10.1016/j.jmaa.2003.09.012Google Scholar
  4. R. T. Rockafellar: Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc. 123 (1966) 46–63.https://doi.org/10.1090/S0002-9947-1966-0192318-XGoogle Scholar
  5. M. Volle: A formula on the conjugate of the max of a convex function and a concave function, J. Math. Anal. Appl. 220 (1998) 313–321.https://doi.org/10.1006/jmaa.1997.5884Google Scholar

Suggested citation

J.-B. Hiriart-Urruty. “Conjugating the Inverse of a Concave Function.” Journal of Convex Analysis 12 (2005), No. 1, 71–79. https://doi.org/10.68381/jca12004

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.