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The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems.
The numerical solution of parabolic elliptic differential equations
D. H. Peaceman and H. H. Rachford · 1955
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On the numerical solution of the heat conduction problem in 2 and 3 space variables
J. Douglas and H. H. Rachford · 1956
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Sur l’approximation par éléments finis et la résolution par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires
R. Glowinski and A. Marrocco · 1975
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A dual algorithm for the solution of nonlinear variational problems via finite-element approximations
D. Gabay and B. Mercier · 1976
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Splitting algorithms for the sum of two nonlinear operators
P. L. Lions and B. Mercier · 1979
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Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems
M. Fortin and R. Glowinski · 1983
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Applications of the method of multipliers to variational inequalities
D. Gabay · 1983
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Splitting methods for monotone operators with applications to parallel optimization
J. Eckstein · 1989
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Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics
R. Glowinski and P. Le Tallec · 1989
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On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
J. Eckstein and D. P. Bertsekas · 1992
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Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Recovering low-rank and sparse components of matrices from incomplete and noisy observations
M. Tao and X. Yuan · 2011
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A note on the alternating direction method of multipliers
D. Han and X. Yuan · 2012
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Alternating direction method with Gaussian back substitution for separable convex programming
B. He, M. Tao, and X. Yuan · 2012
Cited alongside, same era.
On the O ( 1 / n ) {O}(1/n) convergence rate of Douglas-Rachford alternating direction method
B. He and X. Yuan · 2012
Cited alongside, same era.
On the linear convergence of the alternating direction method of multipliers
M. Hong and Z. Luo · 2012
Cited alongside, same era.
RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images
Y. Peng, A. Ganesh, J. Wright, W. Xu, and Y. Ma · 2012
Cited alongside, same era.
Local linear convergence of the alternating direction method of multipliers on quadratic or linear programs
D. Boley · 2013
Cited alongside, same era.
The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent
C. Chen, B. He, Y. Ye, and X. Yuan · 2014
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Faster convergence rates of relaxed Peaceman-Rachford and ADMM under regularity assumptions
D. Davis and W. Yin · 2014
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M. Hong, T.-H. Chang, X. Wang, M. Razaviyayn, S. Ma, and Z.-Q. Luo · 2014
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A three-operator splitting scheme and its optimization applications
D. Davis and W. Yin · 2015
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On the global and linear convergence of the generalized alternating direction method of multipliers
W. Deng and W. Yin · 2015
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On the convergence analysis of the alternating direction method of multipliers with three blocks
C. Chen, Y. Shen, and Y. You · 2013
Cited alongside, same era.
Parallel multi-block ADMM with o ( 1 / k ) o(1/k) convergence
W. Deng, M. Lai, Z. Peng, and W. Yin · 2013
Cited alongside, same era.
On full Jacobian decomposition of the augmented Lagrangian method for separable convex programming
B. He, L. Hou, and X. Yuan · 2013
Cited alongside, same era.
Convergence rate and iteration complexity on the alternating direction method of multipliers with a substitution procedure for separable convex programming
B. He, M. Tao, and X. Yuan · 2013
Cited alongside, same era.
Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers
R. D. C. Monteiro and B. F. Svaiter · 2013
Cited alongside, same era.
X. Wang, M. Hong, S. Ma, and Z.-Q. Luo · 2013
Cited alongside, same era.
The direct extension of ADMM for three-block separable convex minimization models is convergent when one function is strongly convex
X. Cai, D. Han, and X. Yuan · 2014
Cited alongside, same era.
Augmented lagrangian and alternating direction methods for convex optimization: A tutorial and some illustrative computational results
J. Eckstein and W. Yao · 2015
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On nonergodic convergence rate of Douglas-Rachford alternating direction method of multipliers
B. He and X. Yuan · 2015
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A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block
M. Li, D. Sun, and K.-C. Toh · 2015
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Global convergence of unmodified 3-block ADMM for a class of convex minimization problems
T. Lin, S. Ma, and S. Zhang · 2015
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T. Lin, S. Ma, and S. Zhang · 2015
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On the global linear convergence of the ADMM with multi-block variables
T. Lin, S. Ma, and S. Zhang · 2015
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A convergent 3-block semiproximal alternating direction method of multipliers for conic programming with 4-type constraints
D. Sun, K.-C. Toh, and L. Yang · 2015
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