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<p>The symmetric alternating direction method of multipliers (SADMM) is a flexible and efficient method for solving two-block convex optimization problems which are widely used in engineering fields. However, SADMM or its directly extended version may fail to converge when either the involved number of blocks is more than two, or there is a nonconvex term in the objective function. This paper proposes a distributed multi-block partially symmetric Bregman ADMM algorithm (MPSB-ADMM) for solving the nonconvex sharing problem, which employs Bregman distance in each subproblem and updates the dual variable twice in each iteration. We show that the sequence generated by the proposed method converges to a critical point of the considered problem under some mild conditions. In addition, the strong convergence is established with the help of Kurdyka-Łojasiewicz inequality. Finally, the effectiveness is verified by a preliminary numerical experiment.</p>

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Distributed Multi-block Partially Symmetric Bregman ADMM for Nonconvex and Nonsmooth Sharing Problem

  • 期刊论文

  • 发表日期：

    2025年3月7日

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  • Tian-Tian Cui,
  • Ya-Zheng Dang,
  • Yan Gao

摘要

The symmetric alternating direction method of multipliers (SADMM) is a flexible and efficient method for solving two-block convex optimization problems which are widely used in engineering fields. However, SADMM or its directly extended version may fail to converge when either the involved number of blocks is more than two, or there is a nonconvex term in the objective function. This paper proposes a distributed multi-block partially symmetric Bregman ADMM algorithm (MPSB-ADMM) for solving the nonconvex sharing problem, which employs Bregman distance in each subproblem and updates the dual variable twice in each iteration. We show that the sequence generated by the proposed method converges to a critical point of the considered problem under some mild conditions. In addition, the strong convergence is established with the help of Kurdyka-Łojasiewicz inequality. Finally, the effectiveness is verified by a preliminary numerical experiment.