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Convex Analysis and Monotone Operator Theory in Hilbert Spaces pp 263–287Cite as

Subdifferentiability of Convex Functions

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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.

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References

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

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Kelowna, BC, Canada

    Heinz H. Bauschke

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Patrick L. Combettes

Authors
  1. Heinz H. Bauschke
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  2. Patrick L. Combettes
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Bauschke, H.H., Combettes, P.L. (2017). Subdifferentiability of Convex Functions. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_16

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