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Global convergence of a non-convex Douglas–Rachford iteration

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Abstract

We establish a region of convergence for the proto-typical non-convex Douglas–Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, pp. 93–109, 2011) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

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Authors and Affiliations

  1. Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW, 2308, Australia

    Francisco J. Aragón Artacho & Jonathan M. Borwein

  2. King Abdul-Aziz University, Jeddah, Saudi Arabia

    Jonathan M. Borwein

Authors
  1. Francisco J. Aragón Artacho
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  2. Jonathan M. Borwein
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Correspondence to Francisco J. Aragón Artacho.

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Aragón Artacho, F.J., Borwein, J.M. Global convergence of a non-convex Douglas–Rachford iteration. J Glob Optim 57, 753–769 (2013). https://doi.org/10.1007/s10898-012-9958-4

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  • DOI: https://doi.org/10.1007/s10898-012-9958-4

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