IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v89y2024i2d10.1007_s10898-023-01348-y.html
   My bibliography  Save this article

A Bregman inertial forward-reflected-backward method for nonconvex minimization

Author

Listed:
  • Xianfu Wang

    (University of British Columbia)

  • Ziyuan Wang

    (University of British Columbia)

Abstract

We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One distinguishing feature in our analysis is that we utilize a careful treatment of merit function parameters, circumventing the usual restrictive assumption on the inertial parameters. We also present formulae for the Bregman subproblem, supplementing not only BiFRB but also the work of Boţ-Csetnek-László and Boţ-Csetnek. Numerical simulations are conducted to evaluate the performance of our proposed algorithm.

Suggested Citation

  • Xianfu Wang & Ziyuan Wang, 2024. "A Bregman inertial forward-reflected-backward method for nonconvex minimization," Journal of Global Optimization, Springer, vol. 89(2), pages 327-354, June.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:2:d:10.1007_s10898-023-01348-y
    DOI: 10.1007/s10898-023-01348-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-023-01348-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/s10898-023-01348-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. Radu Ioan Bot & Dang-Khoa Nguyen, 2020. "The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 682-712, May.
    2. Radu Ioan Boţ & Ernö Robert Csetnek & Szilárd Csaba László, 2016. "An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(1), pages 3-25, February.
    3. Xianfu Wang & Ziyuan Wang, 2022. "Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems," Computational Optimization and Applications, Springer, vol. 82(2), pages 441-463, June.
    4. Peter Ochs, 2018. "Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 153-180, April.
    5. Xianfu Wang & Ziyuan Wang, 2022. "The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 2765-2783, November.
    6. Chen Chen & Ting Kei Pong & Lulin Tan & Liaoyuan Zeng, 2020. "A difference-of-convex approach for split feasibility with applications to matrix factorizations and outlier detection," Journal of Global Optimization, Springer, vol. 78(1), pages 107-136, September.
    Full references (including those not matched with items on IDEAS)

    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. Xianfu Wang & Ziyuan Wang, 2022. "Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems," Computational Optimization and Applications, Springer, vol. 82(2), pages 441-463, June.
    2. Szilárd Csaba László, 2023. "A Forward–Backward Algorithm With Different Inertial Terms for Structured Non-Convex Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 387-427, July.
    3. Ziyuan Wang & Andreas Themelis & Hongjia Ou & Xianfu Wang, 2024. "A Mirror Inertial Forward–Reflected–Backward Splitting: Convergence Analysis Beyond Convexity and Lipschitz Smoothness," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1127-1159, November.
    4. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    5. Dolgopolik, Maksim V., 2021. "The alternating direction method of multipliers for finding the distance between ellipsoids," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    6. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
    7. Emanuel Laude & Peter Ochs & Daniel Cremers, 2020. "Bregman Proximal Mappings and Bregman–Moreau Envelopes Under Relative Prox-Regularity," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 724-761, March.
    8. Eyal Cohen & Nadav Hallak & Marc Teboulle, 2022. "A Dynamic Alternating Direction of Multipliers for Nonconvex Minimization with Nonlinear Functional Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 324-353, June.
    9. Boţ, Radu Ioan & Kanzler, Laura, 2021. "A forward-backward dynamical approach for nonsmooth problems with block structure coupled by a smooth function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    10. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization," Computational Optimization and Applications, Springer, vol. 79(3), pages 681-715, July.
    11. Yong-Jin Liu & Jing Yu, 2022. "A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 749-779, December.
    12. Zhijian Lai & Akiko Yoshise, 2022. "Completely positive factorization by a Riemannian smoothing method," Computational Optimization and Applications, Springer, vol. 83(3), pages 933-966, December.
    13. Yingting Zhang & Zewei Huang, 2022. "Application of multimedia network english listening model based on confidence learning algorithm for speech recognition," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1091-1101, December.
    14. Camille Castera, 2023. "Inertial Newton Algorithms Avoiding Strict Saddle Points," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 881-903, December.
    15. 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.
    16. Masaru Ito & Bruno F. Lourenço, 2024. "Eigenvalue programming beyond matrices," Computational Optimization and Applications, Springer, vol. 89(2), pages 361-384, November.
    17. Zhongming Wu & Min Li & David Z. W. Wang & Deren Han, 2017. "A Symmetric Alternating Direction Method of Multipliers for Separable Nonconvex Minimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-27, December.
    18. Le Thi Khanh Hien & Dimitri Papadimitriou, 2024. "An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints," Journal of Global Optimization, Springer, vol. 89(4), pages 927-948, August.
    19. Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
    20. Zhili Ge & Zhongming Wu & Xin Zhang & Qin Ni, 2023. "An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 821-844, August.

    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:jglopt:v:89:y:2024:i:2:d:10.1007_s10898-023-01348-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.