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Extrapolation algorithm for affine-convex feasibility problems

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The convex feasibility problem under consideration is to find a common point of a countable family of closed affine subspaces and convex sets in a Hilbert space. To solve such problems, we propose a general parallel block-iterative algorithmic framework in which the affine subspaces are exploited to introduce extrapolated over-relaxations. This framework encompasses a wide range of projection, subgradient projection, proximal, and fixed point methods encountered in various branches of applied mathematics. The asymptotic behavior of the method is investigated and numerical experiments are provided to illustrate the benefits of the extrapolations.

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Authors and Affiliations

  1. Mathematics, Irving K. Barber School, UBC Okanagan, Kelowna, BC, V1V 1V7, Canada

    Heinz H. Bauschke

  2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris 6, 75005, Paris, France

    Patrick L. Combettes

  3. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309-4485, USA

    Serge G. Kruk

Authors
  1. Heinz H. Bauschke
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  2. Patrick L. Combettes
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  3. Serge G. Kruk
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Correspondence to Heinz H. Bauschke.

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Communicated by Claude Brezinski

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Bauschke, H.H., Combettes, P.L. & Kruk, S.G. Extrapolation algorithm for affine-convex feasibility problems. Numer Algor 41, 239–274 (2006). https://doi.org/10.1007/s11075-005-9010-6

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