Numerical Algorithms

, Volume 41, Issue 3, pp 239–274

Extrapolation algorithm for affine-convex feasibility problems

  • Heinz H. Bauschke
  • Patrick L. Combettes
  • Serge G. Kruk

DOI: 10.1007/s11075-005-9010-6

Cite this article as:
Bauschke, H.H., Combettes, P.L. & Kruk, S.G. Numer Algor (2006) 41: 239. doi:10.1007/s11075-005-9010-6

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 setsconvex feasibility problemconvex setsextrapolationHilbert spaceProjection method

AMS subject classification


Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Heinz H. Bauschke
    • 1
  • Patrick L. Combettes
    • 2
  • Serge G. Kruk
    • 3
  1. 1.Mathematics, Irving K. Barber SchoolUBC OkanaganKelownaCanada
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie, Paris 6ParisFrance
  3. 3.Department of Mathematics and StatisticsOakland UniversityRochesterUSA