Distributed alternating direction method of multipliers (ADMM) is a widely used algorithm for large-scale optimization problems due to its fast convergence rate. However, most studies implement the distributed ADMM by communicating with all neighbor nodes, which assumably ignores the communication cost. In this paper, we propose a novel distributed ADMM algorithm with synergetic communication and computation, called SCCD-ADMM, as an attempt to reduce the total cost of the system. Specifically, each node searches the number of communication nodes considering both the communication and computation cost, chooses a subset of its neighbor nodes to receive messages from and then updates the local variables using a newly designed update rule, to attain proper trade-off between the costs of communication and computation. Numerical experiments validate that total cost can be greatly saved in SCCD-ADMM compared with the traditional distributed ADMM, especially in the case where the communication is costly.
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