IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i16p2630-d1725916.html
   My bibliography  Save this article

A New Proximal Iteratively Reweighted Nuclear Norm Method for Nonconvex Nonsmooth Optimization Problems

Author

Listed:
  • Zhili Ge

    (School of Mathematical Sciences, Nanjing Normal University of Special Education, Nanjing 210038, China)

  • Siyu Zhang

    (School of Microelectronics and Data Science, Anhui University of Technology, Ma’anshan 243032, China)

  • Xin Zhang

    (School of Mathematics and Physics, Suqian University, Suqian 223800, China
    Key Laboratory of Numerical Simulation for Large Scale Complex Systems, Ministry of Education, Nanjing 210023, China)

  • Yan Cui

    (School of Artificial Intelligence, Nanjing Normal University of Special Education, Nanjing 210038, China)

Abstract

This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality reduction and extrapolation. This strategy overcomes parameter constraints by enabling adaptive dynamic adjustment of the extrapolation/proximal parameters ( α k , β k , μ k ). Under the Kurdyka–Łojasiewicz framework for nonconvex and nonsmooth optimization, we prove the global convergence and linear convergence rate of the proposed algorithm. Additionally, through numerical experiments using synthetic and real data in matrix completion problems, we validate the superior performance of the proposed method over well-known methods.

Suggested Citation

  • Zhili Ge & Siyu Zhang & Xin Zhang & Yan Cui, 2025. "A New Proximal Iteratively Reweighted Nuclear Norm Method for Nonconvex Nonsmooth Optimization Problems," Mathematics, MDPI, vol. 13(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2630-:d:1725916
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/16/2630/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/16/2630/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Ting Tao & Lianghai Xiao & Jiayuan Zhong, 2025. "A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers," Mathematics, MDPI, vol. 13(9), pages 1-15, April.
    3. Xian Zhang & Dingtao Peng & Yanyan Su, 2024. "A singular value shrinkage thresholding algorithm for folded concave penalized low-rank matrix optimization problems," Journal of Global Optimization, Springer, vol. 88(2), pages 485-508, February.
    4. Ke Guo & Deren Han, 2018. "A note on the Douglas–Rachford splitting method for optimization problems involving hypoconvex functions," Journal of Global Optimization, Springer, vol. 72(3), pages 431-441, November.
    5. 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.
    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. 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.
    2. Zhongming Wu & Chongshou Li & Min Li & Andrew Lim, 2021. "Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 79(3), pages 617-644, March.
    3. Yonghong Yao & Sani Salisu & Zai-Yun Peng & Yekini Shehu, 2025. "New Splitting Algorithm with Three Inertial Steps for Three-Operator Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-28, September.
    4. Xin Yang & Lingling Xu, 2023. "Some accelerated alternating proximal gradient algorithms for a class of nonconvex nonsmooth problems," Journal of Global Optimization, Springer, vol. 87(2), pages 939-964, November.
    5. Min Li & Zhongming Wu, 2019. "Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 535-565, November.
    6. 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.
    7. Chih-Sheng Chuang & Hongjin He & Zhiyuan Zhang, 2022. "A unified Douglas–Rachford algorithm for generalized DC programming," Journal of Global Optimization, Springer, vol. 82(2), pages 331-349, February.
    8. 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.
    9. Lulu He & Jimin Ye & E. Jianwei, 2023. "Accelerated Stochastic Variance Reduction for a Class of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 810-828, March.
    10. Hongwei Liu & Ting Wang & Zexian Liu, 2024. "A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems," Journal of Global Optimization, Springer, vol. 89(4), pages 863-897, August.
    11. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jmathe:v:13:y:2025:i:16:p:2630-:d:1725916. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.