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The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two maximally monotone operators.
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J.-B. Baillon and G. Haddad, Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones, Israel Journal of Mathematics 26 (1977), 137–150
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P.L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM Journal on Numerical Analysis 16 (1979), 964–979
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D. Gabay, Applications of the method of multipliers to variational inequalities. In: M. Fortin, R. Glowinski (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems , 299–331. North-Holland, Amsterdam (1983)
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K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory , Cambridge University Press, Cambridge, 1990
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E. Zeidler, Nonlinear Functional Analysis and Its Applications II/A: Linear Monotone Operators , Springer-Verlag, 1990
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E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B: Nonlinear Monotone Operators , Springer-Verlag, 1990
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J. Eckstein and D.P. Bertsekas, On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming 55 (1992), 293–318
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P.L. Combettes, The convex feasibility problem in image recovery, Advances in Imaging and Electron Physics 25 (1995), 155–270
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S. Simons, Minimax and Monotonicity , Springer-Verlag, 1998
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P.L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization 53 (2004), 475–504
2004
Cited alongside, same era.
R.S. Burachik and A.N. Iusem, Set-Valued Mappings and Enlargements of Monotone Operators , Springer-Verlag, 2008
2008
Cited alongside, same era.
S. Simons, From Hahn-Banach to Monotonicity , Springer-Verlag, 2008
2008
Cited alongside, same era.
R.T. Rockafellar and R. J-B Wets, Variational Analysis , Springer-Verlag, corrected 3rd printing, 2009
2009
Cited alongside, same era.
H.H. Bauschke and P.L. Combettes, The Baillon–Haddad theorem revisited, Journal of Convex Analysis 17 (2010), 781–787
2010
Cited alongside, same era.
J.M. Borwein, Fifty years of maximal monotonicity, Optimization Letters 4 (2010), 473–490
R. Hesse and D.R. Luke, Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems, SIAM journal on Optimization 23 (2013), 2397–2419
2013
Later among the works it cites.
H.H. Bauschke, J.Y. Bello Cruz, T.T.A. Nghia, H.M. Phan, and X. Wang, The rate of linear convergence of the Douglas–Rachford algorithm for subspaces is the cosine of the Friedrichs angle, Journal of Approximation Theory 185 (2014), 63–79
2014
Later among the works it cites.
R. Hesse, D.R. Luke and P. Neumann, Alternating projections and Douglas–Rachford for sparse affine feasibility, IEEE Transactions of Signal Processing 62 (2014), 4868–4881
2014
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D. O’Connor and L. Vandenberghe, Primal-dual decomposition by operator splitting and applications to image deblurring, SIAM Journal on Imaging Sciences 7 (2014), no. 3, 1724–1754
2014
Later among the works it cites.
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2010
Cited alongside, same era.
L.M. Briceño-Arias and P.L. Combettes, A monotone + skew splitting model for composite monotone inclusions in duality, SIAM Journal on Optimization 21 (2011), 1230–1250
2011
Cited alongside, same era.
B.F. Svaiter, On weak convergence of the Douglas–Rachford method, SIAM Journal on Control and Optimization 49 (2011), 280–287
2011
Cited alongside, same era.
P.L. Combettes and J.-C. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued and Variational Analysis 20 (2012), 307–330
2012
Cited alongside, same era.
R.I. Boţ and C. Hendrich, A Douglas–Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators, SIAM Journal on Optimization 23 (2013), 2541–2565
2013
Cited alongside, same era.
L. Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms, Journal of Optimization Theory and Applications 158 (2013), 460–479
2013
Cited alongside, same era.
L. Demanet and X. Zhang, Eventual linear convergence of the Douglas–Rachford iteration for basis pursuit, to appear in Mathematics of Computation, AMS
Cited in the paper.
T. Aspelmeier, C. Charitha, and D. Russell Luke, Local Linear Convergence of the ADMM/Douglas–Rachford Algorithms without Strong Convexity and Application to Statistical Imaging, SIAM Journal on Imaging Sciences 9 (2016), 842–868
2016
Later among the works it cites.
H.H. Bauschke and W.M. Moursi, The Douglas–Rachford algorithm for two (not necessarily intersecting) affine subspaces, SIAM Journal on Optimization 26 (2016), 968–985
2016
Later among the works it cites.
H.M. Phan, Linear convergence of the Douglas–Rachford method for two closed sets, Optimization 65 (2016), 36–385
2016
Later among the works it cites.
H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces , Second Edition, Springer, 2017
2017
Later among the works it cites.
P. Giselsson, Tight global linear convergence rate bounds for Douglas–Rachford splitting, Journal of Fixed Point Theory and Applications , 2017. DOI 10.1007/s11784-0170417-1
2017
Later among the works it cites.
P. Giselsson, S. Boyd, Linear convergence and metric selection for Douglas–Rachford splitting and ADMM, IIEEE Transactions on Automatic Control 62 (2017), 532–544
2017
Later among the works it cites.
Wolfram Research, Inc., Mathematica
2018
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