论文标题
使用ADMM的快速共识权重的分布式计算
Distributed computation of fast consensus weights using ADMM
论文作者
论文摘要
我们考虑了在多个代理之间达到平均共识的问题，在该代理中，图形互通信网络被图表描绘出来。我们考虑离散时间共识协议，每个代理都将其值更新为其自身价值的加权平均值和其邻居的价值。鉴于图，众所周知，存在一组“最佳权重”，因此代理商以最佳的收敛速度渐近地达成平均共识。但是，现有方法需要整个图的知识来计算这些最佳权重。我们为每个代理商提出了一种计算本地最佳权重的方法，即，每个代理只需要知道谁是邻居。该方法是通过使用乘数的交替方向方法（ADMM）来求解矩阵规范最小化问题，以分布式方式受到线性约束。我们使用数值示例说明了结果，并将我们的方法与现有的方法（称为大都市权重）进行了比较，该方法也在本地计算。
We consider the problem of achieving average consensus among multiple agents, where the inter-agent communication network is depicted by a graph. We consider the discrete-time consensus protocol where each agent updates its value as a weighted average of its own value and those of its neighbours. Given a graph, it is known that there exists a set of 'optimal weights' such that the agents reach average consensus asymptotically with an optimal rate of convergence. However, existing methods require the knowledge of the entire graph to compute these optimal weights. We propose a method for each agent to compute its set of optimal weights locally, i.e., each agent only has to know who are its neighbours. The method is derived by solving a matrix norm minimization problem subject to linear constraints in a distributed manner using the Alternating Direction Method of Multipliers (ADMM). We illustrate our results using numerical examples and compare our method with an existing method called the Metropolis weights, which are also computed locally.
