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The Douglas--Rachford method is a splitting method frequently employed for finding zeroes of sums of maximally monotone operators.
Functional Operators
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The numerical solution of parabolic and elliptic differential equations
Donald W. Peaceman and Henry H Rachford, Jr · 1955
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On the numerical solution of heat conduction problems in two and three space variables
Jim Douglas, Jr. and H. H. Rachford, Jr · 1956
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Kenneth J. Arrow, Leonid Hurwicz, and Hirofumi Uzawa · 1958
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Projection Algorithms for Non-separable Wavelets and Clifford Fourier Analysis
David J. Franklin · 1959
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A finite-difference method of high-order accuracy for the solution of three-dimensional transient heat conduction problems
P.L.T. Brian · 1961
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The method of successive projection for finding a common point of convex sets
Lev M. Bregman · 1965
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Projections on convex sets in Hilbert space and spectral theory: Part I. projections on convex sets: Part II. spectral theory
Eduardo H. Zarantonello · 1971
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Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires
Roland Glowinski and A. Marroco · 1975
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
Daniel Gabay and Bertrand Mercier · 1976
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Conjugate duality and optimization
R. Tyrrell Rockafellar · 1976
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Monotone operators and the proximal point algorithm
R Tyrrell Rockafellar · 1976
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Finite element approximation and iterative solution of a class of mildly non-linear elliptic equations
Tony Fan C. Chan and Roland Glowinski · 1978
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On the maximality of the sum of two maximal monotone operators
Hedy Attouch · 1979
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Splitting algorithms for the sum of two nonlinear operators
P.-L. Lions and B. Mercier · 1979
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Phase retrieval algorithms: a comparison
James R. Fienup · 1982
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Applications of the method of multipliers to variational inequalities
Daniel Gabay · 1983
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Partial inverse of a monotone operator
Jonathan E. Spingarn · 1983
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Decomposition through formalization in a product space
Guy Pierra · 1984
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A relaxed projection method for variational inequalities
Masao Fukushima · 1986
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Splitting methods for monotone operators with applications to parallel optimization
Jonathan Eckstein · 1989
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On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators
Jonathan Eckstein and Dimitri P. Bertsekas · 1992
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On projection algorithms for solving convex feasibility problems
Heinz H. Bauschke and Jonathan M. Borwein · 1996
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The primal Douglas–Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
Masao Fukushima · 1996
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Visual Complex Analysis
Tristan Needham · 1997
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Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems
Michel Fortin and Roland Glowinski · 2000
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From parallel to sequential projection methods and vice versa in convex feasibility: results and conjectures
Alvaro R. De Pierro · 2001
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Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization
Heinz H. Bauschke, Patrick L. Combettes, and D. Russell Luke · 2002
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Hybrid projection–reflection method for phase retrieval
Heinz H. Bauschke, Patrick L. Combettes, and D. Russell Luke · 2003
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Phase retrieval by iterated projections
Veit Elser · 2003
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The Hundal example revisited
Eva Matoušková and Simeon Reich · 2003
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Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
Heinz H. Bauschke, Patrick L. Combettes, and D. Russell Luke · 2004
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Solving monotone inclusions via compositions of nonexpansive averaged operators
Patrick L. Combettes · 2004
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An alternating projection that does not converge in norm
Hein S. Hundal · 2004
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A new proximal point iteration that converges weakly but not in norm
Heinz H. Bauschke, J. Burke, F. Deutsch, H. Hundal, and J. Vanderwerff · 2005
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Convex Analysis and Nonlinear Optimization: Theory and Examples
Jonathan M. Borwein and Adrian S. Lewis · 2006
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About regularity of collections of sets
Alexander Y. Kruger · 2006
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A Douglas–Rachford splitting approach to nonsmooth convex variational signal recovery
Patrick L. Combettes and Jean-Christophe Pesquet · 2007
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Searching with iterated maps
Veit Elser, I. Rankenburg, and P. Thibault · 2007
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A family of projective splitting methods for the sum of two maximal monotone operators
Jonathan Eckstein and Benar Fux Svaiter · 2008
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Divide and concur: A general approach to constraint satisfaction
Simon Gravel and Veit Elser · 2008
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General projective splitting methods for sums of maximal monotone operators
Jonathan Eckstein and Benar Fux Svaiter · 2009
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The split Bregman method for L1-regularized problems
Tom Goldstein and Stanley Osher · 2009
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Local linear convergence for alternating and averaged nonconvex projections
Adrian S. Lewis, D. Russell Luke, and Jérôme Malick · 2009
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Split Bregman algorithm, Douglas–Rachford splitting and frame shrinkage
Simon Setzer · 2009
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Code for solving tetravex using Douglas–Rachford algorithm, 2010
Pulkit Bansal · 2010
Cited alongside, same era.
Modeling the 8-queens problem and sudoku using an algorithm based on projections onto nonconvex sets
Jason Schaad · 2010
Cited alongside, same era.
Removing multiplicative noise by Douglas–Rachford splitting methods
Gabriele Steidl and Tanja Teuber · 2010
Cited alongside, same era.
Convex analysis and monotone operator theory in Hilbert spaces
Heinz H. Bauschke and Patrick L. Combettes · 2011
Cited alongside, same era.
The Douglas–Rachford algorithm in the absence of convexity
Jonathan M. Borwein and Brailey Sims · 2011
Cited alongside, same era.
Proximal splitting methods in signal processing
Patrick L. Combettes and Jean-Christophe Pesquet · 2011
Cited alongside, same era.
On the order of the operators in the Douglas–Rachford algorithm
Heinz H. Bauschke and Walaa M. Moursi · 2016
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New Douglas–Rachford algorithmic structures and their convergence analyses
Yair Censor and Rafiq Mansour · 2016
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Convergence rate analysis of several splitting schemes
Damek Davis and Wotao Yin · 2016
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Eventual linear convergence of the Douglas–Rachford iteration for basis pursuit
Laurent Demanet and Xiangxiong Zhang · 2016
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Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
Guoyin Li and Ting Kei Pong · 2016
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The Douglas–Rachford operator in the possibly inconsistent case: static properties and dynamic behaviour
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On weak convergence of the Douglas–Rachford method
Benar F. Svaiter · 2011
Cited alongside, same era.
Attouch–Théra duality revisited: paramonotonicity and operator splitting
Heinz H. Bauschke, Radu I. Boţ, Warren L. Hare, and Walaa M. Moursi · 2012
Cited alongside, same era.
Reflection methods for inverse problems with applications to protein conformation determination
Jonathan M. Borwein and Matthew K. Tam · 2012
Cited alongside, same era.
Iterative methods for fixed point problems in Hilbert spaces
Andrzej Cegielski · 2012
Cited alongside, same era.
On the O(1/n) convergence rate of the Douglas–Rachford alternating direction method
Bingsheng He and Xiaoming Yuan · 2012
Cited alongside, same era.
Global convergence of a non-convex Douglas–Rachford iteration
Francisco J. Aragón Artacho and Jonathan M Borwein · 2013
Cited alongside, same era.
Walaa M. Moursi · 2016
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Linear convergence of the Douglas–Rachford method for two closed sets
Hung M. Phan · 2016
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Iterative projection and reflection methods: theory and practice
Matthew K. Tam · 2016
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On the finite convergence of the Douglas–Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces
Heinz H. Bauschke and Minh N. Dao · 2017
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Affine nonexpansive operators, Attouch–Théra duality and the Douglas–Rachford algorithm
Heinz H. Bauschke, Brett Lukens, and Walaa M. Moursi · 2017
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On the Douglas–Rachford algorithm
Heinz H. Bauschke and Walaa M. Moursi · 2017
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Ergodic behaviour of a Douglas–Rachford operator away from the origin
Jonathan M. Borwein and Ohad Giladi · 2017
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Matrix product constraints by projection methods
Veit Elser · 2017
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Optimal convergence rates for generalized alternating projections
Mattias Fält and Pontus Giselsson · 2017
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Tight global linear convergence rate bounds for Douglas–Rachford splitting
Pontus Giselsson · 2017
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Linear convergence and metric selection for Douglas–Rachford splitting and ADMM
Pontus Giselsson and Stephen Boyd · 2017
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Splitting methods in communication, imaging, science, and engineering
Roland Glowinski, Stanley J. Osher, and Wotao Yin · 2017
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Local convergence of proximal splitting methods for rank constrained problems
Christian Grussler and Pontus Giselsson · 2017
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Computing intersections of implicitly specified plane curves
Scott B. Lindstrom, Brailey Sims, and Matthew P. Skerritt · 2017
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Phase retrieval, what’s new
D. Russell Luke · 2017
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Finding maximum rank moment matrices by facial reduction on primal form and Douglas–Rachford iteration
Fei Wang, Greg Reid, and Henry Wolkowicz · 2017
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On the asymptotic behaviour of the Aragón Artacho–Campoy algorithm
Salihah Alwadani, Heinz H. Bauschke, Walaa M. Moursi, and Xianfu Wang · 2018
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A new projection method for finding the closest point in the intersection of convex sets
Francisco J. Aragón Artacho and Rubén Campoy · 2018
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Solving graph coloring problems with the Douglas–Rachford algorithm
Francisco J. Aragón Artacho and Rubén Campoy · 2018
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A feasibility approach for constructing combinatorial designs of circulant type
Francisco J. Aragón Artacho, Rubén Campoy, Ilias Kotsireas, and Matthew K. Tam · 2018
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An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm
FJ Artacho, Rubén Campoy, and Veit Elser · 2018
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On Douglas–Rachford operators that fail to be proximal mappings
Heinz H. Bauschke, Jason Schaad, and Xianfu Wang · 2018
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On the linear convergence of the circumcentered-reflection method
Roger Behling, José Yunier Bello-Cruz, and L-R Santos · 2018
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Circumcentering the Douglas–Rachford method
Roger Behling, José Yunier Bello Cruz, and Luiz-Rafael Santos · 2018
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Dynamics of the Douglas–Rachford method for ellipses and p-spheres
Jonathan M. Borwein, Scott B. Lindstrom, Brailey Sims, Matthew Skerritt, and Anna Schneider · 2018
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The complexity of bit retrieval
Veit Elser · 2018
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Benchmark problems for phase retrieval
Veit Elser, Ti-Yen Lan, and Tamir Bendory · 2018
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About intrinsic transversality of pairs of sets
Alexander Y. Kruger · 2018
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Douglas–Rachford splitting for a lipschitz continuous and a strongly monotone operator
Walaa M Moursi and Lieven Vandenberghe · 2018
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Douglas–Rachford splitting and ADMM for nonconvex optimization: tight convergence results
Andreas Themelis and Panos Patrinos · 2018
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Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm
Francisco J. Aragón Artacho and Rubén Campoy · 2019
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The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators
Francisco J. Aragón Artacho, Yair Censor, and Aviv Gibali · 2019
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The Douglas–Rachford algorithm for a hyperplane and a doubleton
Heinz H. Bauschke, Minh N. Dao, and Scott B. Lindstrom · 2019
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Adaptive Douglas–Rachford splitting algorithm for the sum of two operators
Minh N. Dao and Hung M. Phan · 2019
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Linear convergence of projection algorithms
Minh N. Dao and Hung M. Phan · 2019
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Application of projection algorithms to differential equations: boundary value problems
Bishnu P. Lamichhane, Scott B. Lindstrom, and Brailey Sims · 2019
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A note on the equivalence of operator splitting methods
Walaa M. Moursi and Yuriy Zinchenko · 2019
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A weakly convergent fully inexact douglas-rachford method with relative error tolerance
Benar Fux Svaiter · 2019
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Comparing averaged relaxed cutters and projection methods: Theory and examples
Reinier R Díaz Millán, Scott B. Lindstrom, and Vera Roshchina · 2020
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