Set-Valued Analysis

, Volume 1, Issue 2, pp 185–212 | Cite as

On the convergence of von Neumann's alternating projection algorithm for two sets

  • H. H. Bauschke
  • J. M. Borwein


We give several unifying results, interpretations, and examples regarding the convergence of the von Neumann alternating projection algorithm for two arbitrary closed convex nonempty subsets of a Hilbert space. Our research is formulated within the framework of Fejér monotonicity, convex and set-valued analysis. We also discuss the case of finitely many sets.

Mathematics Subject Classifications (1991)

Primary 47H09, 65J05 secondary 41A25, 41A50, 46C99, 47N10, 49M45, 65Kxx, 90C25 

Key words

Algorithm von Neumann's algorithm method alternating method iterative method projection cyclic projections successive projections Hilbert space convex sets linear convergence norm convergence weak convergence open mapping theorem multifunctions convex relations convex feasibility problem least-squares approximation angle between two subspaces 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • H. H. Bauschke
    • 1
  • J. M. Borwein
    • 2
  1. 1.Department of Mathematics, Statistics and Computing ScienceDalhousie UniversityHalifaxCanada
  2. 2.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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