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Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions.
The numerical solution of parabolic and elliptic differential equations
D. W. Peaceman and H. H. Rachford · 1955
Earlier work this paper cites.
On the numerical solution of heat conduction problems in two and three space variables
J. Douglas and H. H. Rachford · 1956
Earlier work this paper cites.
Convex Analysis
R. T. Rockafellar · 1970
Earlier work this paper cites.
Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problémes de dirichlet non linéaires
R. Glowinski and A. Marroco · 1975
Earlier work this paper cites.
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.
Splitting algorithms for the sum of two nonlinear operators
P. L. Lions and B. Mercier · 1979
Earlier work this paper cites.
Applications of the method of multipliers to variational inequalities
D. Gabay · 1983
Earlier work this paper cites.
On the global and linear convergence of the generalized alternating direction method of multipliers
W. Deng and W. Yin · 2012
Cited alongside, same era.
On the o ( 1 / n ) o(1/n) convergence rate of the Douglas-Rachford alternating direction method
B. He and X. Yuan · 2012
Cited alongside, same era.
Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit
L. Demanet and X. Zhang · 2013
Cited alongside, same era.
E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson · 2013
Cited alongside, same era.
On the linear convergence of the alternating direction method of multipliers
M. Hong and Z.-Q. Luo · 2013
Faster convergence rates of relaxed Peaceman-Rachford and ADMM under regularity assumptions
D. Davis and W. Yin · 2014
Later among the works it cites.
Diagonal scaling in Douglas-Rachford splitting and ADMM
P. Giselsson and S. Boyd · 2014
Later among the works it cites.
Metric selection in Douglas-Rachford splitting and ADMM
P. Giselsson and S. Boyd · 2014
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Douglas-Rachford splitting: Complexity estimates and accelerated variants
P. Patrinos, L. Stella, and A. Bemporad · 2014
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ADMM for convex quadratic programs: Linear convergence and infeasibility detection
A. Raghunathan and S. Di Cairano · 2014
Later among the works it cites.
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Cited alongside, same era.
Functional Analysis
Michel Willem · 2013
Cited alongside, same era.
Convergence rate analysis of several splitting schemes
D. Davis and W. Yin · 2014
Cited alongside, same era.
R. Nishihara, L. Lessard, B. Recht, A. Packard, and M. Jordan · 2015
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