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Global convergence of a non-convex Douglas–Rachford iteration

Author

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  • Francisco Aragón Artacho
  • Jonathan Borwein

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Francisco Aragón Artacho & Jonathan Borwein, 2013. "Global convergence of a non-convex Douglas–Rachford iteration," Journal of Global Optimization, Springer, vol. 57(3), pages 753-769, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:753-769
    DOI: 10.1007/s10898-012-9958-4
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    Cited by:

    1. Chih-Sheng Chuang & Hongjin He & Zhiyuan Zhang, 2022. "A unified Douglas–Rachford algorithm for generalized DC programming," Journal of Global Optimization, Springer, vol. 82(2), pages 331-349, February.
    2. Francisco J. Aragón Artacho & Rubén Campoy & Matthew K. Tam, 2020. "The Douglas–Rachford algorithm for convex and nonconvex feasibility problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 201-240, April.

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