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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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