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Applied Mathematics and Computation, ISSN 0096-3003, 04/2015, Volume 256, pp. 472 - 487
Journal Article
Operations Research Letters, ISSN 0167-6377, 03/2018, Volume 46, Issue 2, pp. 159 - 162
In order to accelerate the Douglas–Rachford method we recently developed the circumcentered-reflection method, which provides the closest iterate to the... 
Projection | Reflection | Best approximation problem | Douglas–Rachford method | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FEASIBILITY | DOUGLAS-RACHFORD ALGORITHM | SUBSPACES | ALTERNATING PROJECTIONS | Mathematics - Optimization and Control
Journal Article
Operations Research Letters, ISSN 0167-6377, 07/2019, Volume 47, Issue 4, pp. 291 - 293
Douglas–Rachford method is a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Weak convergence in this method to a solution... 
Weak convergence | Monotone operators | Douglas–Rachford method | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUM | Methods | Algorithms
Journal Article
Journal of optimization theory and applications, ISSN 1573-2878, 2013, Volume 163, Issue 1, pp. 1 - 30
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 05/2018, Volume 44, Issue 3, pp. 665 - 699
The Fourier-domain Douglas–Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution... 
Geometric convergence | Douglas–Rachford algorithm | Coded diffraction pattern | Spectral gap | Phase retrieval | MATHEMATICS, APPLIED | MAGNITUDE | Douglas-Rachford algorithm | RECONSTRUCTION | SIGNAL RECOVERY | RAY | spectral gap | geometric convergence | coded diffraction pattern
Journal Article
Signal processing, ISSN 0165-1684, 2020, Volume 169, p. 107417
•Proximal algorithms with sound convergence are proposed to solve matrix estimation problems.•New proximity operators for spectral functions within Bregman... 
Majorization-minimization | Graphical lasso | Matrix optimization | Bregman divergence | Covariance estimation | Douglas–Rachford method | Douglas-Rachford method | SPARSE | ITERATIVE ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | COVARIANCE-MATRIX | MINIMIZATION | MODEL SELECTION | CONVERGENCE | Engineering Sciences | Signal and Image processing
Journal Article
The ANZIAM journal, ISSN 1446-1811, 01/2019, Volume 61, Issue 1, pp. 23 - 46
The Douglas–Rachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent research has shown... 
MATHEMATICS, APPLIED | Douglas-Rachford method | hypersurface | DOUGLAS-RACHFORD ALGORITHM | Newton's method | boundary value problem | LINEAR CONVERGENCE
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2016, Volume 85, Issue 297, pp. 209 - 238
We provide a simple analysis of the Douglas-Rachford splitting algorithm in the context of \ell ^1-regularization and over-relaxation including the dual split... 
Asymptotic linear convergence rate | Douglas-Rachford | Peaceman-Rachford | Basis pursuit | Generalized Douglas-Rachford | Relaxation parameter | MATHEMATICS, APPLIED | generalized Douglas-Rachford | relaxation parameter | SPLIT BREGMAN METHOD | ALGORITHM | asymptotic linear convergence rate | SUM
Journal Article
The ANZIAM journal, ISSN 1446-1811, 04/2014, Volume 55, Issue 4, pp. 299 - 326
In this paper, we give general recommendations for successful application of the Douglas–Rachford reflection method to convex and nonconvex real matrix... 
protein reconstruction | Hadamard matrices | feasibility problems | matrix completion | reflections | Phrases Douglas-Rachford projections | MATHEMATICS, APPLIED | APPROXIMATION | Douglas-Rachford projections | CONVERGENCE | ALTERNATING PROJECTION ALGORITHM | Feasibility | Reflection | Guidelines | Mathematics - Optimization and Control
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2015, Volume 421, Issue 1, pp. 1 - 20
We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong... 
Douglas–Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2015, Volume 25, Issue 3, pp. 1760 - 1786
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 09/2014, Volume 185, pp. 63 - 79
The Douglas–Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it... 
Projection operator | Linear convergence | Method of alternating projections | Firmly nonexpansive | Normal cone operator | Subspaces | Douglas–Rachford splitting method | Friedrichs angle | Secondary | Primary | Douglas-Rachford splitting method | MATHEMATICS | Analysis | Algorithms
Journal Article
SIAM journal on optimization, ISSN 1095-7189, 2013, Volume 23, Issue 4, pp. 2541 - 2565
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone... 
Fenchel duality | Monotone inclusion | Convex optimization | Douglas-Rachford splitting | MATHEMATICS, APPLIED | SPLITTING ALGORITHM | convex optimization | GENERALIZED HERON PROBLEM | monotone inclusion
Journal Article
Operations Research Letters, ISSN 0167-6377, 11/2018, Volume 46, Issue 6, pp. 585 - 587
Aragón Artacho and Campoy recently proposed a new method for computing the projection onto the intersection of two closed convex sets in Hilbert space;... 
Maximally monotone operator | Douglas–Rachford algorithm | Resolvent average | Convex function | Proximal average | Aragón Artacho–Campoy algorithm | Aragon Artacho-Campoy algorithm | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | RESOLVENT | AVERAGE | SUM | Electrical engineering | Analysis | Algorithms
Journal Article
Optimization letters, ISSN 1862-4480, 2018, Volume 13, Issue 4, pp. 717 - 740
We shed light on the structure of the three-operator version of the forward-Douglas-Rachford splitting algorithm for finding a zero of a sum of maximally... 
Douglas–Rachford splitting | Nonsmooth convex optimization | Proximal splitting | Monotone operator splitting | Forward–backward splitting | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford splitting | Forward-backward splitting | Algorithms
Journal Article