IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v75y2020i2d10.1007_s10589-019-00165-y.html
   My bibliography  Save this article

Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms

Author

Listed:
  • M. Marques Alves

    (Universidade Federal de Santa Catarina)

  • Jonathan Eckstein

    (Rutgers Business School Newark and New Brunswick)

  • Marina Geremia

    (Universidade Federal de Santa Catarina)

  • Jefferson G. Melo

    (Universidade Federal de Goiás)

Abstract

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact version of the proximal point algorithm that includes both an inertial step and overrelaxation. We apply our new inexact ADMM method to LASSO and logistic regression problems and obtain somewhat better computational performance than earlier inexact ADMM methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00165-y
    DOI: 10.1007/s10589-019-00165-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00165-y
    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/s10589-019-00165-y?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. Dettling, Marcel & Bühlmann, Peter, 2004. "Finding predictive gene groups from microarray data," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 106-131, July.
    2. Jonathan Eckstein & Wang Yao, 2017. "Approximate ADMM algorithms derived from Lagrangian splitting," Computational Optimization and Applications, Springer, vol. 68(2), pages 363-405, November.
    3. 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.
    4. Hedy Attouch & Alexandre Cabot, 2020. "Convergence rate of a relaxed inertial proximal algorithm for convex minimization," Post-Print hal-02415789, HAL.
    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. Mauricio Romero Sicre, 2020. "On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 991-1019, July.
    2. Jamilu Abubakar & Poom Kumam & Abdulkarim Hassan Ibrahim & Anantachai Padcharoen, 2020. "Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    3. 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.
    4. Majela Pentón Machado & Mauricio Romero Sicre, 2023. "A Projective Splitting Method for Monotone Inclusions: Iteration-Complexity and Application to Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 552-587, August.
    5. Yunier Bello-Cruz & Max L. N. Gonçalves & Nathan Krislock, 2023. "On FISTA with a relative error rule," Computational Optimization and Applications, Springer, vol. 84(2), pages 295-318, March.
    6. S.-M. Grad & F. Lara & R. T. Marcavillaca, 2023. "Relaxed-inertial proximal point type algorithms for quasiconvex minimization," Journal of Global Optimization, Springer, vol. 85(3), pages 615-635, March.

    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. Mostafa Rezaei & Ivor Cribben & Michele Samorani, 2021. "A clustering-based feature selection method for automatically generated relational attributes," Annals of Operations Research, Springer, vol. 303(1), pages 233-263, August.
    2. 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.
    3. 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.
    4. William W. Hager & Hongchao Zhang, 2020. "Convergence rates for an inexact ADMM applied to separable convex optimization," Computational Optimization and Applications, Springer, vol. 77(3), pages 729-754, December.
    5. Zambom, Adriano Zanin & Akritas, Michael G., 2015. "Nonparametric significance testing and group variable selection," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 51-60.
    6. 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.
    7. Dang Hieu & Pham Ky Anh & Nguyen Hai Ha, 2021. "Regularization Proximal Method for Monotone Variational Inclusions," Networks and Spatial Economics, Springer, vol. 21(4), pages 905-932, December.
    8. Fan Wu & Wei Bian, 2023. "Smoothing Accelerated Proximal Gradient Method with Fast Convergence Rate for Nonsmooth Convex Optimization Beyond Differentiability," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 539-572, May.
    9. 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.
    10. Xue Gao & Xingju Cai & Deren Han, 2020. "A Gauss–Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 863-887, April.
    11. Bing Tan & Shanshan Xu & Songxiao Li, 2020. "Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    12. Jessie J Hsu & Dianne M Finkelstein & David A Schoenfeld, 2015. "Outcome-Driven Cluster Analysis with Application to Microarray Data," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-15, November.
    13. Bingsheng He & Feng Ma & Xiaoming Yuan, 2020. "Optimally linearizing the alternating direction method of multipliers for convex programming," Computational Optimization and Applications, Springer, vol. 75(2), pages 361-388, March.
    14. Seakweng Vong & Zhongsheng Yao, 2024. "Modified general splitting method for the split feasibility problem," Journal of Global Optimization, Springer, vol. 90(3), pages 711-726, November.
    15. William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.
    16. Dongying Wang & Xianfu Wang, 2019. "A parameterized Douglas–Rachford algorithm," Computational Optimization and Applications, Springer, vol. 73(3), pages 839-869, July.
    17. Patrick R. Johnstone & Pierre Moulin, 2017. "Local and global convergence of a general inertial proximal splitting scheme for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 259-292, June.
    18. Lateef Olakunle Jolaoso & Maggie Aphane, 2020. "A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    19. 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.
    20. Cui, Qiurong & Xu, Yuqing & Zhang, Zhengjun & Chan, Vincent, 2021. "Max-linear regression models with regularization," Journal of Econometrics, Elsevier, vol. 222(1), pages 579-600.

    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:75:y:2020:i:2:d:10.1007_s10589-019-00165-y. 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.