Journal of Global Optimization

, Volume 65, Issue 2, pp 309–327 | Cite as

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

  • Francisco J. Aragón ArtachoEmail author
  • Jonathan M. Borwein
  • Matthew K. Tam


In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.


Douglas–Rachford algorithm Global convergence Feasibility problem Half-space Non-convex 

Mathematics Subject Classification

90C26 65K05 



We would like to thank the anonymous referee for their helpful suggestions and comments.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Francisco J. Aragón Artacho
    • 1
    Email author
  • Jonathan M. Borwein
    • 2
  • Matthew K. Tam
    • 2
  1. 1.Department of MathematicsUniversity of AlicanteAlicanteSpain
  2. 2.Centre for Computer-Assisted Research Mathematics and its Applications (CARMA)University of NewcastleCallaghanAustralia

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