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Distributed forward-backward methods for ring networks

Author

Listed:
  • Francisco J. Aragón-Artacho

    (University of Alicante)

  • Yura Malitsky

    (Linköping University)

  • Matthew K. Tam

    (University of Melbourne)

  • David Torregrosa-Belén

    (University of Alicante)

Abstract

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable for distributed, decentralised implementation in ring networks without needing global summation to enforce consensus between nodes.

Suggested Citation

  • Francisco J. Aragón-Artacho & Yura Malitsky & Matthew K. Tam & David Torregrosa-Belén, 2023. "Distributed forward-backward methods for ring networks," Computational Optimization and Applications, Springer, vol. 86(3), pages 845-870, December.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:3:d:10.1007_s10589-022-00400-z
    DOI: 10.1007/s10589-022-00400-z
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    References listed on IDEAS

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    1. Patrick R. Johnstone & Jonathan Eckstein, 2021. "Single-forward-step projective splitting: exploiting cocoercivity," Computational Optimization and Applications, Springer, vol. 78(1), pages 125-166, January.
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    Cited by:

    1. William W. Hager & R. Tyrrell Rockafellar & Vladimir M. Veliov, 2023. "Preface to Asen L. Dontchev Memorial Special Issue," Computational Optimization and Applications, Springer, vol. 86(3), pages 795-800, December.

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