ADMM
The alternating direction method of multipliers (ADMM) is an algorithm that
solves convex optimization problems by breaking them into smaller pieces, each
of which are then easier to handle. It has recently found wide application in a
number of areas. On this page, we provide a few links to to interesting
applications and implementations of the method, along with a few primary
references.
ADMM is used in a large number of papers at this point, so
it is impossible to be comprehensive here. We only intend to highlight a few
representative examples in different areas. To keep the listing light, we have
only listed more detailed bibliographic information for papers that are not
easy to find online; in any case, the information given should be more than
enough to track down the papers.
Main references
 Distributed optimization and
statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, 2011
 Proximal algorithms
N. Parikh and S. Boyd, 2014
Software
Classic papers
 On the numerical solution of heat conduction problems
in two and three space variables
J. Douglas and H. H. Rachford, Transactions of the American Mathematical Society,
1956
 Sur l'approximation, par éléments finis d'ordre un, et la résolution, par
pénalisationdualité d'une classe de problèmes de Dirichlet non linéares
R. Glowinski and A. Marrocco, Revue Française d'Automatique, Informatique, et Recherche Opérationelle, 1975
 A dual algorithm for the solution of nonlinear
variational problems via finite element approximations
D. Gabay and B. Mercier, Computers and
Mathematics with Applications, 1976
 Splitting algorithms for the sum of two nonlinear operators
P. L. Lions and B. Mercier, 1979
 On the DouglasRachford splitting method and the
proximal point algorithm for maximal monotone operators
J. Eckstein and D. Bertsekas, Mathematical Programming, 1992
Generic problems
 Alternating direction augmented Lagrangian methods for semidefinite programming
Z. Wen, D. Goldfarb, and W. Yin, 2010
 Block splitting for distributed optimization
N. Parikh and S. Boyd, 2014
 Operator splitting for conic optimization via homogeneous
selfdual embedding
B. O'Donoghue, E. Chu, N. Parikh, and S. Boyd, 2014
Applications
 Robust Principal Component Analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright, 2009
 An alternating direction method for dual MAP LP relaxation
O. Meshi and A. Globerson, 2011
 An augmented Lagrangian approach to constrained MAP inference
A. Martins, M. Figueiredo, P. Aguiar, N. Smith, and E. Xing, 2011
 Dual decomposition with many overlapping components
A. F. T. Martins, N. A. Smith, P. M. Q. Aguiar, and M. A. T. Figueiredo, 2011
 Decomposition methods for large scale LP decoding
S. Barman, X. Liu, S. Draper, and B. Recht, 2011
 Scaling MPE inference for constrained continuous Markov random fields with consensus optimization
S. Bach, M. Broecheler, L. Getoor, and D. O'Leary, 2012
 Distributed robust multicell coordinated beamforming with imperfect CSI: an ADMM approach
C. Shen, T.H. Chang, K.Y. Wang, Z. Qiu, and C.Y. Chi, 2012
 Design of optimal sparse feedback gains via the alternating direction method of multipliers
F. Lin, M. Fardad, M. R. Jovanovic, 2013
 Tensor completion for estimating missing values in visual data
J. Liu, P. Musialski, P. Wonka, J. Ye, 2013
 A lasso for hierarchical interactions
J. Bien, J. Taylor, and R. Tibshirani, 2013
 Statistical estimation and testing via the sorted norm
M. Bogdan, E. van den Berg, W. Su and E. J. Candès, 2013
 The joint graphical lasso for inverse covariance estimation across multiple classes
P. Danaher, P. Wang, and D. Witten, 2013
 Distributed robust power system state estimation
V. Kekatos and G. B. Giannakis, 2013
 A splitting method for optimal control
B. O'Donoghue, G. Stathopoulos, and S. Boyd, 2013
 Dynamic network energy management via
proximal message passing
M. Kraning, E. Chu, J. Lavaei, and S. Boyd, 2014
Theory and variations
 On the convergence rate of the DouglasRachford alternating direction method
B. He and X. Yuan, 2012
 Fast alternating direction optimization methods
T. Goldstein, B. O'Donoghue, S. Setzer, and R. Baraniuk, 2012
 Augmented Lagrangian and alternating direction methods for convex optimization: a tutorial and some illustrative computational results
J. Eckstein, 2012
