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Differentiability of Convex Functions

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

Abstract

Fréchet differentiability, Gâteaux differentiability, directional differentiability, subdifferentiability, and continuity are notions that are closely related to each other. In this chapter, we provide fundamental results on these relationships, as well as basic results on the steepest descent direction, the Chebyshev center, and the max formula that relates the directional derivative to the support function of the subdifferential at a given point.

Copyright information

© Springer International Publishing AG 2017

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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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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