Numerical Algorithms

, Volume 41, Issue 3, pp 239-274

First online:

Extrapolation algorithm for affine-convex feasibility problems

  • Heinz H. BauschkeAffiliated withMathematics, Irving K. Barber School, UBC Okanagan Email author 
  • , Patrick L. CombettesAffiliated withLaboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris 6
  • , Serge G. KrukAffiliated withDepartment of Mathematics and Statistics, Oakland University

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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.


affinite sets convex feasibility problem convex sets extrapolation Hilbert space Projection method

AMS subject classification

90C25 47J25 47N10