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Distributed Basis Pursuit

J. F. C. Mota (joaomota***at***cmu.edu)
J. M. F. Xavier (jxavier***at***isr.ist.utl.pt)
P. M. Q. Aguiar (aguiar***at***isr.ist.utl.pt)
M. Püschel (pueschel***at***inf.ethz.ch)

Abstract: We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.

Keywords: Basis pursuit, distributed optimization, sensor networks, augmented Lagrangian

Category 1: Network Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: Appears on IEEE Transaction on Signal Processing, Vol. 60, Issue 4, April, 2012. DOI: 10.1109/TSP.2011.2182347

Download: [PDF]

Entry Submitted: 08/03/2011
Entry Accepted: 09/01/2011
Entry Last Modified: 03/14/2012

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