Distributed ADMM for Time-Varying Communication Networks

The distributed alternating direction method of multipliers (ADMM) is an efficient distributed optimization algorithm, which however shows poor convergence in time-varying network topologies. To solve the challenge, we propose TV-ADMM, a novel distributed ADMM algorithm for time-varying communication networks. More specifically, importance weight parameters are introduced in message fusion, with the purpose of mitigating the potential error brought by the network topology dynamics. Based on that, the updating rules are designed with the first-order approximation and a Bregman divergence term, which can reduce the variance caused by the randomness and enhance the robustness. Moreover, we consider two different practical scenarios with time-varying communication network. In Scenario One, the communication between two nodes succeeds with certain probabilities, based on which the importance weight parameters are designed. Scenario Two considers mobile agents, where the communication link is determined by the distance between two agents. We derive the connectivity probability in this scenario and get the corresponding importance weight. Numerical simulations validate the effectiveness of the proposed algorithm in both scenarios, in comparison with the subgradient-based method.