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Convex Sets

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

Abstract

In this chapter we introduce the fundamental notion of the convexity of a set and establish various properties. The key result is Theorem 3.16, which asserts that every nonempty closed convex subset C of \({\mathcal {H}}\) is a Chebyshev set, i.e., that every point in \({\mathcal {H}}\) possesses a unique best approximation from C, and which provides a characterization of this best approximation.

References

  1. [147]
    F. Deutsch, Best Approximation in Inner Product Spaces, Springer-Verlag, New York, 2001.CrossRefGoogle Scholar

Copyright information

© 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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