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The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency.
Xxv.–on Bernoulli’s numerical solution of algebraic equations
A. C. Aitken · 1927
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Viii. the deferred approach to the limit
L. F. Richardson and J. A. Gaunt · 1927
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The numerical solution of parabolic and elliptic differential equations
D. W. Peaceman and H. H. Rachford, Jr · 1955
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Non-linear transformations of divergent and slowly convergent sequences
D. Shanks · 1955
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On the numerical solution of heat conduction problems in two and three space variables
J. Douglas and H. H. Rachford · 1956
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Acceleration techniques for iterated vector and matrix problems
P. Wynn · 1962
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Iterative procedures for nonlinear integral equations
D. G. Anderson · 1965
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A dual algorithm for the solution of non linear variational problems via finite element approximation
D. Gabay and B. Mercier · 1975
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Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires
R. Glowinski and A. Marroco · 1975
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A polynomial extrapolation method for finding limits and antilimits of vector sequences
S. Cabay and L. W. Jackson · 1976
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Convergence acceleration for the iterative solution of the equations x= ax+ f
M. Mešina · 1977
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Extrapolating to the limit of a vector sequence
R. P. Eddy · 1979
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Chapter ix applications of the method of multipliers to variational inequalities
D. Gabay · 1983
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A method for solving the convex programming problem with convergence rate
Y. Nesterov · 1983
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Acceleration of convergence of vector sequences
A. Sidi, W. F. Ford, and D. A. Smith · 1986
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Introduction to optimization
B. T. Polyak · 1987
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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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Upper bounds for convergence rates of acceleration methods with initial iterations
A. Sidi and Y. Shapira · 1998
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An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
F. Alvarez and H. Attouch · 2001
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Convergence acceleration during the 20th century
C. Brezinski · 2001
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Monic integer chebyshev problem
P. Borwein, C. Pinner, and I. Pritsker · 2003
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Smooth manifolds
J. M. Lee · 2003
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Active sets, nonsmoothness, and sensitivity
A. S. Lewis · 2003
Cited alongside, same era.
Practical extrapolation methods: Theory and applications
A. Sidi · 2003
Cited alongside, same era.
Identifying active constraints via partial smoothness and prox-regularity
A strictly contractive peaceman–rachford splitting method for convex programming
B. He, H. Liu, Z. Wang, and X. Yuan · 2014
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Local linear convergence of Forward–Backward under partial smoothness
J. Liang, J. Fadili, and G. Peyré · 2014
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On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm”
A. Chambolle and C. Dossal · 2015
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Accelerated alternating direction method of multipliers
M. Kadkhodaie, K. Christakopoulou, M. Sanjabi, and A. Banerjee · 2015
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Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas–Rachford methods for two subspaces
H. H. Bauschke, J. Y. Bello Cruz, T. T. A. Nghia, H. M. Pha, and X. Wang · 2016
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W. L. Hare and A. S. Lewis · 2004
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Newton methods for nonsmooth convex minimization: connections among-Lagrangian, Riemannian Newton and SQP methods
S. A. Miller and J. Malick · 2005
Cited alongside, same era.
Riemannian geometry: a modern introduction
I. Chavel · 2006
Cited alongside, same era.
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
Cited alongside, same era.
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
H. Bauschke and P. L. Combettes · 2011
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al · 2011
Cited alongside, same era.
L. Demanet and X. Zhang · 2016
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On the global and linear convergence of the generalized alternating direction method of multipliers
W. Deng and W. Yin · 2016
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Convergence rates of first-order operator splitting methods
J. Liang · 2016
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Accelerated admm based on accelerated douglas-rachford splitting
I. Pejcic and C. N. Jones · 2016
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Regularized nonlinear acceleration
D. Scieur, A. d’Aspremont, and F. Bach · 2016
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On the linear convergence of the alternating direction method of multipliers
M. Hong and Z. Luo · 2017
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Activity identification and local linear convergence of Forward–Backward-type methods
J. Liang, J. Fadili, and G. Peyré · 2017
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Local convergence properties of Douglas–Rachford and alternating direction method of multipliers
J. Liang, J. Fadili, and G. Peyré · 2017
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Vector extrapolation methods with applications
A. Sidi · 2017
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A dynamical systems perspective on nonsmooth constrained optimization
G. Franca, D. P. Robinson, and R. Vidal · 2018
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ADMM and accelerated ADMM as continuous dynamical systems
Guilherme Franca, Daniel Robinson, and Rene Vidal · 2018
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Model consistency of partly smooth regularizers
S. Vaiter, G. Peyré, and J. Fadili · 2018
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