Fast decentralized gradient descent method and applications to in-situ seismic tomography

We consider the decentralized consensus optimization problem arising from in-situ seismic tomography in large-scale sensor networks. Unlike traditional seismic imaging performed in a centralized location, each node in this setting privately holds an objective function and partial data. The goal of each node is to obtain the optimal solution of the whole seismic image, while communicating only with its immediate neighbors. We present a fast decentralized gradient descent method and prove that this new method can reach optimal convergence rate of O(1/k2) where k is the number of communication/iteration rounds. Extensive numerical experiments on synthetic and real-world sensor network seismic data demonstrate that the proposed algorithms significantly outperform existing methods.