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A parameterized Douglas–Rachford algorithm

Author

Listed:
  • Dongying Wang

    (University of British Columbia)

  • Xianfu Wang

    (University of British Columbia
    Southwest University)

Abstract

Based on a reparametrization of the Douglas–Rachford algorithm, we provide a principle of finding the least norm solution for a sum of two maximally monotone operators. The algorithm allows us to find the least norm solution to a sum of monotone operators, and even generally to find the least norm primal-dual solution to inclusions with mixtures of composite monotone operators. Three numerical results illustrate our results.

Suggested Citation

  • Dongying Wang & Xianfu Wang, 2019. "A parameterized Douglas–Rachford algorithm," Computational Optimization and Applications, Springer, vol. 73(3), pages 839-869, July.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:3:d:10.1007_s10589-019-00088-8
    DOI: 10.1007/s10589-019-00088-8
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    References listed on IDEAS

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    1. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
    2. Francisco J. Aragón Artacho & Rubén Campoy, 2018. "A new projection method for finding the closest point in the intersection of convex sets," Computational Optimization and Applications, Springer, vol. 69(1), pages 99-132, January.
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    Cited by:

    1. Tianle Lu & Xue Zhang, 2024. "An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems," Mathematics, MDPI, vol. 12(5), pages 1-24, February.
    2. Bian, Fengmiao & Zhang, Xiaoqun, 2021. "A parameterized Douglas–Rachford splitting algorithm for nonconvex optimization," Applied Mathematics and Computation, Elsevier, vol. 410(C).

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