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Subdifferentiability of Convex Functions

  • Heinz H. Bauschke
  • Patrick L. Combettes
Chapter
  • 2.6k Downloads
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

The subdifferential is a fundamental tool in the analysis of nondifferentiable convex functions. In this chapter we discuss the properties of subdifferentials and the interplay between the subdifferential and the Legendre transform. Moreover, we establish the Brøndsted–Rockafellar theorem, which asserts that the graph of the subdifferential operator is dense in the domain of the separable sum of the function and its conjugate.

References

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    E. Ernst and M. Théra, Boundary half-strips and the strong chip, SIAM J. Optim., 18 (2007), pp. 834–852.MathSciNetCrossRefGoogle Scholar

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© Springer International Publishing AG 2017

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Authors and Affiliations

  • Heinz H. Bauschke
    • 1
  • Patrick L. Combettes
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaKelownaCanada
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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