Convex Sets

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


In this chapter we introduce the fundamental notion of the convexity of a set and establish various properties of convex sets. The key result is Theorem 3.14, 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.


Convex Subset Real Hilbert Space Nonempty Closed Convex Subset Closed Linear Subspace Orthonormal Sequence 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics Irving K. Barber SchoolUniversity of British ColumbiaKelownaCanada
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie - Paris 6ParisFrance

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