We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has a favorable structure suitable for effective computation of the proximal operator. In our method, each agent iteratively updates its estimate of the global minimum by optimizing its local objective function, and exchanging estimates with others via communication in the network. Using Nesterov-type acceleration techniques and multiple communication steps per iteration, we show that this method converges at the rate 1/k (where k is the number of communication rounds between the agents), which is faster than the convergence rate of the existing distributed methods for solving this problem. The superior convergence rate of our method is also verified by numerical experiments.

该研究提出了一种基于分布式近端梯度方法来优化平均凸函数的方法，每个凸函数都是网络中各个代理的本地目标函数。该方法通过交换估计值来实现每个代理迭代更新全局最小值的目标，并使用Nesterov-type加速技术和多个通信步骤进行迭代，表明这种方法的收敛速率为1/k（其中k是代理之间的通信轮数），这比现有的分布式方法的收敛速度更快。数值实验也验证了该方法的卓越收敛速度。

一种快速的分布式近端梯度法