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Best Approximation Algorithms

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

Abstract

Best approximation algorithms were already discussed in Corollary  5.30, in Example  28.18, and in Example  28.19. In this chapter, we provide further approaches for computing the projection onto the intersection of finitely many closed convex sets. The methods we present, all of which employ the individual projectors onto the given sets, are Halpern’s algorithm, Dykstra’s algorithm, and Haugazeau’s algorithm. Applications to solving monotone inclusion and minimization problems with strongly convergent algorithms are also given.

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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