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.
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14 January 2020
The original version of this book was inadvertently published without updating the following corrections in Chapters 1, 2, 3, 6–13, 17, 18, 20, 23, 24, 26, 29, 30 and back matter. These are corrected now.
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© 2017 Springer International Publishing AG
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Bauschke, H.H., Combettes, P.L. (2017). Best Approximation Algorithms. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_30
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DOI: https://doi.org/10.1007/978-3-319-48311-5_30
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48310-8
Online ISBN: 978-3-319-48311-5
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