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A Relaxed Alternating Direction Method Of Multipliers For Separable Nonconvex Minimization Problems

Author

Listed:
  • Jing Zhao

    (Civil Aviation University of China)

  • Chenzheng Guo

    (Xidian University)

  • Xiaolong Qin

    (Hangzhou Normal University
    Academy of Romanian Scientists)

Abstract

The alternating direction method of multipliers (ADMM) is popular and powerful in computing the solutions of various composite minimization problems with constraints. In this paper, we propose a relaxed ADMM with a general dual step-size, which includes the classic ADMM in the algorithm framework, for minimizing separable nonconvex functions with linear constraints. Under some assumptions on the penalty parameter and the objective function, the convergence of the proposed algorithm is obtained based on the Kurdyka–Łojasiewicz property. Moreover, we report some preliminary numerical results on involving matrix decomposition problem to demonstrate the feasibility and effectiveness of the proposed method.

Suggested Citation

  • Jing Zhao & Chenzheng Guo & Xiaolong Qin, 2025. "A Relaxed Alternating Direction Method Of Multipliers For Separable Nonconvex Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-29, October.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:1:d:10.1007_s10957-025-02778-2
    DOI: 10.1007/s10957-025-02778-2
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. 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.
    3. Miantao Chao & Yongxin Zhao & Dongying Liang, 2020. "A Proximal Alternating Direction Method of Multipliers with a Substitution Procedure," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, April.
    4. Danqing Zhou & Haiwen Xu & Junfeng Yang, 2024. "Proximal Alternating Direction Method of Multipliers with Convex Combination Proximal Centers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 41(03), pages 1-28, June.
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