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Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in(0,(1+\sqrt{5})/2) have been recently established in the literature.
On the maximal monotonicity of subdifferential mappings
R. T. Rockafellar · 1970
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Sur l’approximation, par éléments finis d’ordre un, et la résolution, par penalisation-dualité, d’une classe de problèmes de Dirichlet non linéaires
R. Glowinski and A. Marroco · 1975
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
D. Gabay and B. Mercier · 1976
Earlier work this paper cites.
Monotone operators and the proximal point algorithm
R. T. Rockafellar · 1976
Earlier work this paper cites.
Numerical Methods for Nonlinear Variational Problems
R. Glowinski · 1984
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Some saddle-function splitting methods for convex programming
J. Eckstein · 1994
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ϵ \epsilon -enlargements of maximal monotone operators: theory and applications
R. S. Burachik, C. A. Sagastizábal, and B. F. Svaiter · 1999
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A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
M. V. Solodov and B. F. Svaiter · 1999
Earlier work this paper cites.
An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions
M. V. Solodov and B. F. Svaiter · 2000
Earlier work this paper cites.
On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
R. D. C. Monteiro and B. F. Svaiter · 2010
Earlier work this paper cites.
Bregmanized nonlocal regularization for deconvolution and sparse reconstruction
X. Zhang, M. Burger, X. Bresson, and S. Osher · 2010
Cited alongside, same era.
A unified primal-dual algorithm framework based on Bregman iteration
X. Zhang, M. Burger, and S. Osher · 2010
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
Cited alongside, same era.
A first-order primal-dual algorithm for convex problems with applications to imaging
A. Chambolle and T. Pock · 2011
Cited alongside, same era.
Complexity of variants of Tseng’s modified F-B splitting and korpelevich’s methods for hemivariational inequalities with applications to saddle-point and convex optimization problems
R. D. C. Monteiro and B. F. Svaiter · 2011
Cited alongside, same era.
On the global and linear convergence of the generalized alternating direction method of multipliers
W. Deng and W. Yin · 2015
Later among the works it cites.
Generalized alternating direction method of multipliers: new theoretical insights and applications
E. X. Fang, B. He, H. Liu, and X. Yuan · 2015
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On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers
B. He and X. Yuan · 2015
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Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems
Y. He and R. D. C. Monteiro · 2015
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An extragradient-based alternating direction method for convex minimization
T. Lin, S. Ma, and S. Zhang · 2015
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On the 𝒪 ( 1 / n ) \mathcal{O}(1/n) convergence rate of the Douglas-Rachford alternating direction method
B. He and X. Yuan · 2012
Cited alongside, same era.
The linearized alternating direction method of multipliers for dantzig selector
X. Wang and X Yuan · 2012
Cited alongside, same era.
Hankel matrix rank minimization with applications to system identification and realization
M. Fazel, T. K. Pong, D. Sun, and P. Tseng · 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.
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization
J. Yang and X. Yuan · 2013
Cited alongside, same era.
Improved pointwise iteration-complexity of a regularized ADMM and of a regularized non-euclidean HPE framework
M. L. N. Gonçalves, J. G. Melo, and R. D. C. Monteiro
Cited in the paper.
A semi-proximal-based strictly contractive Peaceman-Rachford splitting method
Y. Gu, B. Jiang, and H. Deren
Cited in the paper.
An accelerated linearized alternating direction method of multipliers
Y. Ouyang, Y. Chen, G. Lan, and E. Pasiliao Jr · 2015
Later among the works it cites.
On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions
Y. Cui, X. Li, D. Sun, and K. C. Toh · 2016
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An O ( 1 / k ) {O}(1/k) convergence rate for the variable stepsize Bregman operator splitting algorithm
W. W. Hager, M. Yashtini, and H. Zhang · 2016
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An accelerated hpe-type algorithm for a class of composite convex-concave saddle-point problems
Y. He and R. D. C. Monteiro · 2016
Closest in time.