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The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.
D.W. Peaceman and H. H. Rachford, Jr, The numerical solution of parabolic and elliptic differential equations, Journal of the Society for Industrial and Applied Mathematics
1955
Earlier work this paper cites.
J. Douglas and H. H. Rachford, On the numerical solution of heat conduction problems in two and three space variables, Transactions of the American Mathematical Society
1956
Earlier work this paper cites.
D. Gabay and B. Mercier, A dual algorithm for the solution of non linear variational problems via finite element approximation, Institut de recherche d’informatique et d’automatique, 1975
1975
Earlier work this paper cites.
R. Glowinski and A. Marroco, Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires, Revue française d’automatique, informatique, recherche opérationnelle. Analyse numérique
1975
Earlier work this paper cites.
Y. Nesterov, A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) {O}(1/k^{2}) , in Dokl. Akad. Nauk SSSR
1983
Earlier work this paper cites.
J. Eckstein and M. Fukushima, Some reformulations and applications of the alternating direction method of multipliers, in Large scale optimization, Springer, 1994, 115–134
1994
Earlier work this paper cites.
B. He, L.Z. Liao, D. Han, and H. Yang, A new inexact alternating directions method for monotone variational inequalities, Mathematical Programming
2002
Earlier work this paper cites.
R. Rockafellar and R. Wets, Variational Analysis, Springer, 317
2004
Earlier work this paper cites.
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends® in Machine Learning
2011
Earlier work this paper cites.
M. Xu and T. Wu, A class of linearized proximal alternating direction methods, Journal of Optimization Theory and Applications
2011
Earlier work this paper cites.
B. He and X. Yuan, On the O ( 1 / n ) {O}(1/n) convergence rate of the Douglas-Rachford alternating direction method, SIAM Journal on Numerical Analysis
2012
Earlier work this paper cites.
M. Fazel, T. K. Pong, D. Sun, and P. Tseng, Hankel matrix rank minimization with applications to system identification and realization, SIAM Journal on Matrix Analysis and Applications
2013
Earlier work this paper cites.
Y. Nesterov, Gradient methods for minimizing composite functions, Mathematical Programming
2013
Cited alongside, same era.
E. Corman and X. Yuan, A generalized proximal point algorithm and its convergence rate, SIAM Journal on Optimization
2014
Cited alongside, same era.
B. He, H. Liu, Z. Wang, and X. Yuan, A strictly contractive Peaceman–Rachford splitting method for convex programming, SIAM Journal on Optimization
2014
Cited alongside, same era.
2015
Cited alongside, same era.
X. Li and X. Yuan, A proximal strictly contractive Peaceman–Rachford splitting method for convex programming with applications to imaging, SIAM Journal on Imaging Sciences
2015
H. Sun, M. Tian, and M. Sun, The symmetric ADMM with indefinite proximal regularization and its application, Journal of Inequalities and Applications
2017
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Z. Wu, M. Li, D.Z. Wang, and D. Han, A symmetric alternating direction method of multipliers for separable nonconvex minimization problems, Asia-Pacific Journal of Operational Research
2017
Closest in time.
J. Bai, J. Li, F. Xu, and H. Zhang, Generalized symmetric ADMM for separable convex optimization, Computational Optimization and Applications
2018
Closest in time.
B. Gao and F. Ma, Symmetric alternating direction method with indefinite proximal regularization for linearly constrained convex optimization, Journal of Optimization Theory and Applications
2018
Closest in time.
Y. He, H. Li, and X. Liu, Relaxed inertial proximal Peaceman–Rachford splitting method for separable convex programming, Frontiers of Mathematics in China
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2016
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W. Deng and W. Yin, On the global and linear convergence of the generalized alternating direction method of multipliers, Journal of Scientific Computing
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