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This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization.
On the numerical solution of heat conduction problems in two and three space variables
J. Douglas, Jr. and H. H. Rachford, Jr · 1956
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Weak convergence of the sequence of successive approximations for nonexpansive mappings
Z. Opial · 1967
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Sur l’approximation, par éléments finis d’ordre 1 1 , et la résolution, par pénalisation-dualité, d’une classe de problèmes de Dirichlet non linéaires
R. Glowinski and A. Marroco · 1974
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
D. Gabay and B. Mercier · 1976
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R. T. Rockafellar · 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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Michel Fortin and Roland Glowinski · 1983
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Applications of the method of multipliers to variational inequalities
Daniel Gabay · 1983
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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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A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
M. V. Solodov and B. F. Svaiter · 1999
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Fast convex optimization via inertial dynamics with Hessian driven damping
H. Attouch, J. Peypouquet, and P. Redont · 2016
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Approximate ADMM algorithms derived from Lagrangian splitting
J. Eckstein and W. Yao · 2017
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Convergence of a relaxed inertial forward-backward algorithm for structured monotone inclusions
H. Attouch and A. Cabot · 2018
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Convergence of a relaxed inertial proximal algorithm for maximally monotone operators
H. Attouch and A. Cabot · 2018
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Relative-error approximate versions of Douglas-Rachford splitting and special cases of the ADMM
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Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions
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