A linearized Bregman algorithm for decentralized basis pursuit

Submitted to a conference

• Technical report

Overview

We solve a decentralized basis pursuit problem in a multiagent system, where each agent holds part of the linear observations on a common sparse vector, and all the agents collaborate to recover the sparse vector through limited neighbor-to-neighbor communication.

The proposed decentralized linearized Bregman algorithm solves the Lagrange dual of an augmented model that is equivalent to basis pursuit. The fact that this dual problem is unconstrained and differentiable enables a lightweight yet efficient decentralized gradient algorithm.

We prove nearly linear convergence of the algorithm in the sense that uniformly for every agent , the error obeys and , where and are independent of or . Numerical experiments demonstrate this convergence.

Citation

K. Yuan, Q. Ling, W. Yin, A. Ribeiro, A linearized Bregman algorithm for decentralized basis pursuit, preprint, 2013.