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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 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.

Keywords

Convex Subset Real Hilbert Space Nonempty Closed Convex Subset Closed Linear Subspace Orthonormal Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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