A linearized bregman algorithm for decentralized basis pursuit

Kun Yuan, Qing Ling, Wotao Yin, Alejandro Ribeiro

Abstract: In this paper 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. The agents collaborate to recover the sparse vector through limited neighboring communication. The proposed decentralized linearized Bregman algorithm solves the Lagrange dual of an augmented ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> 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 dual and primal variables to their optima. Numerical experiments demonstrate the effectiveness of the proposed algorithm.