Journal of optimization theory and applications, ISSN 1573-2878, 2012, Volume 158, Issue 2, pp. 460 - 479

...–backward and Douglas–Rachford methods, as well as the recent primal–dual method of Chambolle and Pock designed for problems with linear composite terms.

Monotone inclusion | Mathematics | Theory of Computation | Optimization | Primal–dual algorithm | Douglas–Rachford method | Proximal method | Fenchel–Rockafellar duality | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Forward–backward method | Operator splitting | Applications of Mathematics | Engineering, general | Convex and nonsmooth optimization | Douglas-Rachford method | Primal-dual algorithm | Fenchel-Rockafellar duality | Forward-backward method | MATHEMATICS, APPLIED | DECOMPOSITION | SUM | ALGORITHMS | RECOVERY | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Convex analysis | Formulations | Operators | Splitting | Composite functions | Inversions | Linear operators | Optimization and Control | Engineering Sciences | Signal and Image processing

Monotone inclusion | Mathematics | Theory of Computation | Optimization | Primal–dual algorithm | Douglas–Rachford method | Proximal method | Fenchel–Rockafellar duality | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Forward–backward method | Operator splitting | Applications of Mathematics | Engineering, general | Convex and nonsmooth optimization | Douglas-Rachford method | Primal-dual algorithm | Fenchel-Rockafellar duality | Forward-backward method | MATHEMATICS, APPLIED | DECOMPOSITION | SUM | ALGORITHMS | RECOVERY | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Convex analysis | Formulations | Operators | Splitting | Composite functions | Inversions | Linear operators | Optimization and Control | Engineering Sciences | Signal and Image processing

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 | Monotone operators | Douglas–Rachford method | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUM | Methods | Algorithms

Weak convergence | Monotone operators | Douglas–Rachford method | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUM | Methods | Algorithms

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2015, Volume 153, Issue 2, pp. 715 - 722

...–Rachford operator splitting method for finding a root of the sum of two maximal monotone set-valued operators...

Mathematical Methods in Physics | 65N12 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Convergence rate | 65K10 | Mathematics | Combinatorics | Douglas–Rachford operator splitting method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford operator splitting method | MONOTONE | ALGORITHM | Yuan (China) | Methods | Studies | Mathematical programming

Mathematical Methods in Physics | 65N12 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Convergence rate | 65K10 | Mathematics | Combinatorics | Douglas–Rachford operator splitting method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford operator splitting method | MONOTONE | ALGORITHM | Yuan (China) | Methods | Studies | Mathematical programming

Journal Article

Numerical Algorithms, ISSN 1017-1398, 7/2018, Volume 78, Issue 3, pp. 759 - 776

We introduce and study a geometric modification of the Douglas–Rachford method called the Circumcentered–Douglas–Rachford method...

65K05 | Secondary 90C25 | Numeric Computing | Projection and reflection operators | Theory of Computation | Best approximation problem | Friedrichs angle | Douglas–Rachford method | 65B99 | Linear convergence | Algorithms | Algebra | Numerical Analysis | Primary 49M27 | Computer Science | Subspaces | MATHEMATICS, APPLIED | Douglas-Rachford method | FEASIBILITY | ALGORITHMS | ALTERNATING PROJECTIONS | Mathematics - Optimization and Control

65K05 | Secondary 90C25 | Numeric Computing | Projection and reflection operators | Theory of Computation | Best approximation problem | Friedrichs angle | Douglas–Rachford method | 65B99 | Linear convergence | Algorithms | Algebra | Numerical Analysis | Primary 49M27 | Computer Science | Subspaces | MATHEMATICS, APPLIED | Douglas-Rachford method | FEASIBILITY | ALGORITHMS | ALTERNATING PROJECTIONS | Mathematics - Optimization and Control

Journal Article

Journal of global optimization, ISSN 1573-2916, 2015, Volume 65, Issue 2, pp. 309 - 327

.... In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering...

Non-convex | Global convergence | 65K05 | Douglas–Rachford algorithm | Mathematics | 90C26 | Operation Research/Decision Theory | Computer Science, general | Feasibility problem | Optimization | Real Functions | Half-space | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | ALGORITHM | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Feasibility | Combinatorics | Mathematical analysis | Half spaces | Empirical analysis | Combinatorial analysis | Convergence | Mathematics - Optimization and Control

Non-convex | Global convergence | 65K05 | Douglas–Rachford algorithm | Mathematics | 90C26 | Operation Research/Decision Theory | Computer Science, general | Feasibility problem | Optimization | Real Functions | Half-space | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | ALGORITHM | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Feasibility | Combinatorics | Mathematical analysis | Half spaces | Empirical analysis | Combinatorial analysis | Convergence | Mathematics - Optimization and Control

Journal Article

Journal of global optimization, ISSN 1573-2916, 2018, Volume 73, Issue 4, pp. 801 - 824

.... Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas...

Nonexpansive operator | Monotone inclusion | Bounded perturbation resilience | Forward–backward splitting method | Mathematics | Optimization | Douglas–Rachford splitting method | Davis–Yin splitting method | Backward–forward splitting method | Operations Research/Decision Theory | Multi-step inertial Krasnosel’skiǐ–Mann algorithm | Computer Science, general | Real Functions | SUPERIORIZATION | MATHEMATICS, APPLIED | Forward-backward splitting method | Backward-forward splitting method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT METHODS | Multi-step inertial Krasnosel'skii-Mann algorithm | Douglas-Rachford splitting method | Davis-Yin splitting method | Splitting | Hilbert space | Algorithms | Iterative methods | Convergence

Nonexpansive operator | Monotone inclusion | Bounded perturbation resilience | Forward–backward splitting method | Mathematics | Optimization | Douglas–Rachford splitting method | Davis–Yin splitting method | Backward–forward splitting method | Operations Research/Decision Theory | Multi-step inertial Krasnosel’skiǐ–Mann algorithm | Computer Science, general | Real Functions | SUPERIORIZATION | MATHEMATICS, APPLIED | Forward-backward splitting method | Backward-forward splitting method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT METHODS | Multi-step inertial Krasnosel'skii-Mann algorithm | Douglas-Rachford splitting method | Davis-Yin splitting method | Splitting | Hilbert space | Algorithms | Iterative methods | Convergence

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 182, Issue 2, pp. 606 - 639

Over the past decades, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency...

Forward–Backward | 65K05 | Mathematics | Theory of Computation | Bregman distance | Optimization | Finite identification | Partial smoothness | Calculus of Variations and Optimal Control; Optimization | 49J52 | 90C25 | Operations Research/Decision Theory | Forward–Douglas–Rachford | 65K10 | Applications of Mathematics | Engineering, general | Local linear convergence | MATHEMATICS, APPLIED | SMOOTHNESS | ALGORITHM | Forward-Douglas-Rachford | DESCENT METHODS | Forward-Backward | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ERROR-BOUNDS | CONVEX MINIMIZATION | Analysis | Methods | Machine learning | Operators (mathematics) | Manifolds | Economic models | Splitting | Divergence | Inverse problems | Image processing | Signal processing | Iterative methods | Convergence | Signal and Image Processing | Information Theory | Functional Analysis | Numerical Analysis | Computer Science | Optimization and Control | Statistics | Statistics Theory | Machine Learning

Forward–Backward | 65K05 | Mathematics | Theory of Computation | Bregman distance | Optimization | Finite identification | Partial smoothness | Calculus of Variations and Optimal Control; Optimization | 49J52 | 90C25 | Operations Research/Decision Theory | Forward–Douglas–Rachford | 65K10 | Applications of Mathematics | Engineering, general | Local linear convergence | MATHEMATICS, APPLIED | SMOOTHNESS | ALGORITHM | Forward-Douglas-Rachford | DESCENT METHODS | Forward-Backward | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ERROR-BOUNDS | CONVEX MINIMIZATION | Analysis | Methods | Machine learning | Operators (mathematics) | Manifolds | Economic models | Splitting | Divergence | Inverse problems | Image processing | Signal processing | Iterative methods | Convergence | Signal and Image Processing | Information Theory | Functional Analysis | Numerical Analysis | Computer Science | Optimization and Control | Statistics | Statistics Theory | Machine Learning

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2013, Volume 163, Issue 1, pp. 1 - 30

...J Optim Theory Appl (2014) 163:1–30 DOI 10.1007/s10957-013-0488-0 Recent Results on Douglas–Rachford Methods for Combinatorial Optimization Problems Francisco...

Mathematics | Theory of Computation | Projections | Combinatorial optimization | Optimization | Nonograms | Calculus of Variations and Optimal Control; Optimization | Sudoku | Operations Research/Decision Theory | Douglas–Rachford | Modelling | Feasibility | Applications of Mathematics | Engineering, general | Satisfiability | Reflections | Douglas-Rachford | MATHEMATICS, APPLIED | ALGORITHM | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEAK-CONVERGENCE | Analysis | Methods | Algorithms | Studies | Combinatorics | Combinatorial analysis

Mathematics | Theory of Computation | Projections | Combinatorial optimization | Optimization | Nonograms | Calculus of Variations and Optimal Control; Optimization | Sudoku | Operations Research/Decision Theory | Douglas–Rachford | Modelling | Feasibility | Applications of Mathematics | Engineering, general | Satisfiability | Reflections | Douglas-Rachford | MATHEMATICS, APPLIED | ALGORITHM | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEAK-CONVERGENCE | Analysis | Methods | Algorithms | Studies | Combinatorics | Combinatorial analysis

Journal Article

Optimization, ISSN 1029-4945, 2015, Volume 65, Issue 2, pp. 369 - 385

In this paper, we investigate the Douglas-Rachford method (DR) for two closed (possibly nonconvex) sets in Euclidean spaces...

superregularity | Douglas-Rachford method | affine-hull reduction | Fejér monotonicity | linear regularity | Secondary: 47H09 | Primary: 49M27 | strong regularity | R-linear convergence | Douglas–Rachford method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | ALGORITHMS | PROJECTIONS | Fejer monotonicity | Euclidean space | Direct reduction | Topology | Regularity | Optimization | Images | Convergence

superregularity | Douglas-Rachford method | affine-hull reduction | Fejér monotonicity | linear regularity | Secondary: 47H09 | Primary: 49M27 | strong regularity | R-linear convergence | Douglas–Rachford method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | ALGORITHMS | PROJECTIONS | Fejer monotonicity | Euclidean space | Direct reduction | Topology | Regularity | Optimization | Images | Convergence

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2019, Volume 74, Issue 1, pp. 67 - 92

We revisit the classical Douglas–Rachford (DR) method for finding a zero of the sum of two maximal monotone operators...

Adaptive step-size | 65K05 | Maximal monotone inclusions | Mathematics | Statistics, general | Optimization | Douglas–Rachford method | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Operations Research, Management Science | Non-stationary iteration | Alternating direction methods of multipliers | 47H05 | 65J15 | SPLITTING METHODS | MATHEMATICS, APPLIED | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SHRINKAGE | ALGORITHMS | SELECTION | Algebra | Management science | Analysis | Methods | Direct reduction | Operators | Computational mathematics | Multipliers | Numerical methods | Convergence

Adaptive step-size | 65K05 | Maximal monotone inclusions | Mathematics | Statistics, general | Optimization | Douglas–Rachford method | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Operations Research, Management Science | Non-stationary iteration | Alternating direction methods of multipliers | 47H05 | 65J15 | SPLITTING METHODS | MATHEMATICS, APPLIED | Douglas-Rachford method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SHRINKAGE | ALGORITHMS | SELECTION | Algebra | Management science | Analysis | Methods | Direct reduction | Operators | Computational mathematics | Multipliers | Numerical methods | Convergence

Journal Article

11.
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The error structure of the Douglas–Rachford splitting method for stiff linear problems

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2016, Volume 303, pp. 140 - 145

.... It is unconditionally stable and is considered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure...

Douglas–Rachford splitting | Order reduction | Inhomogeneous evolution equations | Error analysis | Stiff linear problems | Dissipative operators | Douglas-Rachford splitting | Analysis | Methods | Algorithms | Errors | Splitting | Mathematical analysis | Dissipation | Evolution | Remedies | order reduction | Naturvetenskap | Other Mathematics | error analysis | inhomogeneous evolution equations | Annan matematik | Mathematics | Natural Sciences | Matematik | dissipative operators | stiff linear problems

Douglas–Rachford splitting | Order reduction | Inhomogeneous evolution equations | Error analysis | Stiff linear problems | Dissipative operators | Douglas-Rachford splitting | Analysis | Methods | Algorithms | Errors | Splitting | Mathematical analysis | Dissipation | Evolution | Remedies | order reduction | Naturvetenskap | Other Mathematics | error analysis | inhomogeneous evolution equations | Annan matematik | Mathematics | Natural Sciences | Matematik | dissipative operators | stiff linear problems

Journal Article

International Journal of Computer Vision, ISSN 0920-5691, 5/2011, Volume 92, Issue 3, pp. 265 - 280

We examine the underlying structure of popular algorithms for variational methods used in image processing...

Augmented Lagrangian method | Pattern Recognition | Douglas-Rachford splitting | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Forward-backward splitting | Alternating split Bregman algorithm | Bregman methods | Image denoising | Douglas-rachford splitting | Alternating split bregman algorithm | Augmented lagrangian method | APPROXIMATION | SUM | ITERATIVE ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CONVERGENCE | TOTAL VARIATION MINIMIZATION | SCHEMES | Usage | Image processing equipment industry | Equipment and supplies | Algorithms | Image processing | Methods | Frames | Operators | Splitting | Images | Mathematical models | Shrinkage

Augmented Lagrangian method | Pattern Recognition | Douglas-Rachford splitting | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Forward-backward splitting | Alternating split Bregman algorithm | Bregman methods | Image denoising | Douglas-rachford splitting | Alternating split bregman algorithm | Augmented lagrangian method | APPROXIMATION | SUM | ITERATIVE ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CONVERGENCE | TOTAL VARIATION MINIMIZATION | SCHEMES | Usage | Image processing equipment industry | Equipment and supplies | Algorithms | Image processing | Methods | Frames | Operators | Splitting | Images | Mathematical models | Shrinkage

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2018, Volume 75, Issue 6, pp. 2173 - 2192

A new matched alternating direction implicit (ADI) method is proposed in this paper for solving three-dimensional (3D...

Douglas–Rachford ADI scheme | Matched alternating direction implicit (ADI) method | Parabolic interface problem | Matched interface and boundary (MIB) | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | DIFFUSION EQUATIONS | Douglas-Rachford ADI scheme | SINGULAR SOURCES | ELLIPTIC-EQUATIONS | BOUNDARY MIB METHOD | MATCHED INTERFACE

Douglas–Rachford ADI scheme | Matched alternating direction implicit (ADI) method | Parabolic interface problem | Matched interface and boundary (MIB) | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | DIFFUSION EQUATIONS | Douglas-Rachford ADI scheme | SINGULAR SOURCES | ELLIPTIC-EQUATIONS | BOUNDARY MIB METHOD | MATCHED INTERFACE

Journal Article

Numerical Algorithms, ISSN 1017-1398, 9/2019, Volume 82, Issue 1, pp. 263 - 295

...) method and a Douglas-Rachford-Tseng’s forward-backward (F-B) splitting method for solving two-operator and four-operator monotone inclusions, respectively. The former method...

Monotone operators | Numeric Computing | Theory of Computation | HPE method | Inexact Douglas-Rachford method | Complexity | Splitting | Algorithms | Algebra | 90C25 | Numerical Analysis | Computer Science | Tseng’s forward-backward method | 49M27 | 47H05 | MATHEMATICS, APPLIED | ENLARGEMENT | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | Tseng's forward-backward method | CONVERGENCE | SADDLE-POINT | OPERATORS | Employee motivation | Analysis | Methods

Monotone operators | Numeric Computing | Theory of Computation | HPE method | Inexact Douglas-Rachford method | Complexity | Splitting | Algorithms | Algebra | 90C25 | Numerical Analysis | Computer Science | Tseng’s forward-backward method | 49M27 | 47H05 | MATHEMATICS, APPLIED | ENLARGEMENT | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | Tseng's forward-backward method | CONVERGENCE | SADDLE-POINT | OPERATORS | Employee motivation | Analysis | Methods

Journal Article

15.
Full Text
A new projection method for finding the closest point in the intersection of convex sets

Computational optimization and applications, ISSN 1573-2894, 2017, Volume 69, Issue 1, pp. 99 - 132

In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space...

Convex set | Projection | Mathematics | Reflection | Statistics, general | Best approximation problem | Optimization | Nonexpansive mapping | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Douglas–Rachford algorithm | 47H09 | Operations Research, Management Science | 47N10 | Feasibility problem | Douglas | Rachford algorithm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | FEASIBILITY | LINEAR CONVERGENCE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | REGULARITY | HILBERT-SPACE | ALTERNATING PROJECTIONS | OPERATORS | FIXED-POINTS | Methods | Algorithms | Hilbert space | Convexity | Subspaces | Iterative methods | Internet telephony | Convergence | Mathematics - Optimization and Control

Convex set | Projection | Mathematics | Reflection | Statistics, general | Best approximation problem | Optimization | Nonexpansive mapping | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Douglas–Rachford algorithm | 47H09 | Operations Research, Management Science | 47N10 | Feasibility problem | Douglas | Rachford algorithm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | FEASIBILITY | LINEAR CONVERGENCE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | REGULARITY | HILBERT-SPACE | ALTERNATING PROJECTIONS | OPERATORS | FIXED-POINTS | Methods | Algorithms | Hilbert space | Convexity | Subspaces | Iterative methods | Internet telephony | Convergence | Mathematics - Optimization and Control

Journal Article

Circuits, Systems, and Signal Processing, ISSN 0278-081X, 10/2017, Volume 36, Issue 10, pp. 4022 - 4049

...–Rachford splitting method is a well-known operator splitting method that has been widely applied for solving a certain class of convex composite problems...

Engineering | Compressive sensing | Signal,Image and Speech Processing | Electronics and Microelectronics, Instrumentation | Circuits and Systems | Sparse signal recovery | Douglas–Rachford splitting method | Electrical Engineering | ITERATION | RECONSTRUCTION | SIGNAL RECOVERY | DECOMPOSITION | PRINCIPLES | ENGINEERING, ELECTRICAL & ELECTRONIC | L-MINIMIZATION | CONVEX | PARALLEL ALGORITHMS | CONVERGENCE | Douglas-Rachford splitting method | POINT ALGORITHM | Methods | Algorithms | Economic models | Splitting | Multipliers | Compressive properties | Run time (computers) | Projection | Signal reconstruction | Iterative methods | Detection | Optimization

Engineering | Compressive sensing | Signal,Image and Speech Processing | Electronics and Microelectronics, Instrumentation | Circuits and Systems | Sparse signal recovery | Douglas–Rachford splitting method | Electrical Engineering | ITERATION | RECONSTRUCTION | SIGNAL RECOVERY | DECOMPOSITION | PRINCIPLES | ENGINEERING, ELECTRICAL & ELECTRONIC | L-MINIMIZATION | CONVEX | PARALLEL ALGORITHMS | CONVERGENCE | Douglas-Rachford splitting method | POINT ALGORITHM | Methods | Algorithms | Economic models | Splitting | Multipliers | Compressive properties | Run time (computers) | Projection | Signal reconstruction | Iterative methods | Detection | Optimization

Journal Article