IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v73y2019i3d10.1007_s10589-019-00088-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00088-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00088-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.
    2. Chinedu Izuchukwu & Yekini Shehu, 2021. "New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems Beyond Monotonicity," Networks and Spatial Economics, Springer, vol. 21(2), pages 291-323, June.
    3. Q. L. Dong & J. Z. Huang & X. H. Li & Y. J. Cho & Th. M. Rassias, 2019. "MiKM: multi-step inertial Krasnosel’skiǐ–Mann algorithm and its applications," Journal of Global Optimization, Springer, vol. 73(4), pages 801-824, April.
    4. Seifu Endris Yimer & Poom Kumam & Anteneh Getachew Gebrie & Rabian Wangkeeree, 2019. "Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    5. Francisco J. Aragón Artacho & Rubén Campoy & Matthew K. Tam, 2021. "Strengthened splitting methods for computing resolvents," Computational Optimization and Applications, Springer, vol. 80(2), pages 549-585, November.
    6. Bian, Fengmiao & Zhang, Xiaoqun, 2021. "A parameterized Douglas–Rachford splitting algorithm for nonconvex optimization," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    7. Luis M. Briceño-Arias & Fernando Roldán, 2022. "Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 205-225, October.
    8. Chanjuan Pan & Yuanheng Wang, 2019. "Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    9. Francisco J. Aragón Artacho & Rubén Campoy, 2019. "Computing the Resolvent of the Sum of Maximally Monotone Operators with the Averaged Alternating Modified Reflections Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 709-726, June.
    10. Hedy Attouch & Zaki Chbani & Jalal Fadili & Hassan Riahi, 2022. "Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 704-736, June.
    11. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    12. E. M. Bednarczuk & A. Jezierska & K. E. Rutkowski, 2018. "Proximal primal–dual best approximation algorithm with memory," Computational Optimization and Applications, Springer, vol. 71(3), pages 767-794, December.
    13. Radu Ioan Boţ & Ernö Robert Csetnek, 2016. "An Inertial Tseng’s Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 600-616, November.
    14. M. Marques Alves & Jonathan Eckstein & Marina Geremia & Jefferson G. Melo, 2020. "Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms," Computational Optimization and Applications, Springer, vol. 75(2), pages 389-422, March.
    15. Xiaoqi Yang & Chenchen Zu, 2022. "Convergence of Inexact Quasisubgradient Methods with Extrapolation," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 676-703, June.
    16. Dang Van Hieu & Jean Jacques Strodiot & Le Dung Muu, 2020. "An Explicit Extragradient Algorithm for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 476-503, May.
    17. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
    18. Yekini Shehu & Aviv Gibali, 2020. "Inertial Krasnoselskii–Mann Method in Banach Spaces," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    19. Dang Hieu, 2018. "An inertial-like proximal algorithm for equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 399-415, December.
    20. Yekini Shehu & Aviv Gibali & Simone Sagratella, 2020. "Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 877-894, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:73:y:2019:i:3:d:10.1007_s10589-019-00088-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.