In this article, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the system. Explicitly, in the proposed algorithm, each node interacts with only part of its neighboring nodes, the number of which is progressively determined according to a heuristic searching procedure, which takes into account both the predicted convergence rate and the communication and computation costs at each iteration, resulting in a trade-off between communication and computation. Then the node chooses its neighboring nodes according to an importance sampling distribution derived theoretically to minimize the variance with the latest information it locally stores. Finally, the node updates its local information with a new update rule which adapts to the number of communication nodes. We prove the convergence of the proposed algorithm and provide an upper bound of the convergence variance brought by randomness. Extensive simulations validate the excellent performances of the proposed algorithm in terms of convergence rate and variance, the overall communication and computation cost, the impact of network topology as well as the time for evaluation, in comparison with the traditional counterparts.

中文翻译：

---

具有协同通信和计算功能的分布式 ADMM

在本文中，我们提出了一种具有协同通信和计算的新型分布式交替方向乘法器 (ADMM) 算法，称为 SCCD-ADMM，以降低系统的总通信和计算成本。明确地，在所提出的算法中，每个节点仅与其相邻节点的一部分交互，其数量根据启发式搜索过程逐步确定，该过程考虑了预测的收敛速度以及每次迭代的通信和计算成本，导致通信和计算之间的权衡。然后节点根据理论上导出的重要性采样分布选择其相邻节点，以最小化与其本地存储的最新信息的方差。最后，节点使用适应通信节点数量的新更新规则更新其本地信息。我们证明了所提出算法的收敛性，并提供了随机性带来的收敛方差的上限。与传统算法相比，大量仿真验证了该算法在收敛速度和方差、整体通信和计算成本、网络拓扑的影响以及评估时间方面的优异性能。