SIAM journal on imaging sciences, ISSN 1936-4954, 2013, Volume 6, Issue 3, pp. 1199 - 1226

This paper introduces a generalized forward-backward splitting algorithm for finding a zero of a sum of maximal monotone operators B + Sigma(n)(i=1...

Image processing | Sparsity | Nonsmooth convex optimization | Proximal splitting | Forward-backward algorithm | Monotone operator splitting | nonsmooth convex optimization | image processing | ITERATION | MATHEMATICS, APPLIED | forward-backward algorithm | monotone operator splitting | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | DECOMPOSITION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | sparsity | VARIATIONAL FORMULATION | INVERSE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | proximal splitting | MONOTONE INCLUSIONS | CONVERGENCE | POINT | Operators | Splitting | Proximity | Algorithms | Computation | Mathematical analysis | Imaging | Mathematical models | Mathematics - Optimization and Control | Mathematics | Optimization and Control | Engineering Sciences | Computer Science | Signal and Image processing

Image processing | Sparsity | Nonsmooth convex optimization | Proximal splitting | Forward-backward algorithm | Monotone operator splitting | nonsmooth convex optimization | image processing | ITERATION | MATHEMATICS, APPLIED | forward-backward algorithm | monotone operator splitting | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | DECOMPOSITION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | sparsity | VARIATIONAL FORMULATION | INVERSE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | proximal splitting | MONOTONE INCLUSIONS | CONVERGENCE | POINT | Operators | Splitting | Proximity | Algorithms | Computation | Mathematical analysis | Imaging | Mathematical models | Mathematics - Optimization and Control | Mathematics | Optimization and Control | Engineering Sciences | Computer Science | Signal and Image processing

Journal Article

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

We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function...

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

Applied Mathematics and Computation, ISSN 0096-3003, 04/2015, Volume 256, pp. 472 - 487

We propose an inertial Douglas–Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties...

Douglas–Rachford splitting | Krasnosel’skiı̆–Mann algorithm | Convex optimization | Primal–dual algorithm | Inertial splitting algorithm | Krasnosel'skiѣ-Mann algorithm Primal-dual algorithm Convex optimization | Douglas-Rachford splitting | MATHEMATICS, APPLIED | Primal-dual algorithm | Krasnosel'skii-Mann algorithm | MINIMIZATION | WEAK-CONVERGENCE | PROXIMAL POINT ALGORITHM | OPERATORS | COMPOSITE

Douglas–Rachford splitting | Krasnosel’skiı̆–Mann algorithm | Convex optimization | Primal–dual algorithm | Inertial splitting algorithm | Krasnosel'skiѣ-Mann algorithm Primal-dual algorithm Convex optimization | Douglas-Rachford splitting | MATHEMATICS, APPLIED | Primal-dual algorithm | Krasnosel'skii-Mann algorithm | MINIMIZATION | WEAK-CONVERGENCE | PROXIMAL POINT ALGORITHM | OPERATORS | COMPOSITE

Journal Article

2014, ISBN 3110321432, xvi, 354

Book

Journal of optimization theory and applications, ISSN 1573-2878, 2016, Volume 169, Issue 3, pp. 1042 - 1068

We introduce a first-order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method...

90C06 | Mathematics | Theory of Computation | First-order methods | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Cone programming | Operator splitting | 49M29 | 49M05 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | SETS | DECOMPOSITION | SYSTEMS | INVERSE | Electrical engineering | Computer science | Studies | Mathematical programming | Freeware | Operators | Splitting | Mathematical models | Subspaces | Intersections | Source code

90C06 | Mathematics | Theory of Computation | First-order methods | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Cone programming | Operator splitting | 49M29 | 49M05 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | SETS | DECOMPOSITION | SYSTEMS | INVERSE | Electrical engineering | Computer science | Studies | Mathematical programming | Freeware | Operators | Splitting | Mathematical models | Subspaces | Intersections | Source code

Journal Article

IEEE Transactions on Control Systems Technology, ISSN 1063-6536, 11/2013, Volume 21, Issue 6, pp. 2432 - 2442

We apply an operator splitting technique to a generic linear-convex optimal control problem, which results in an algorithm that alternates between solving a quadratic control problem, for which there...

Algorithm design and analysis | Matrix decomposition | Sparse matrices | fixed point algorithms for control | model predictive control (MPC) | Alternating directions method of multipliers (ADMM) | Optimal control | convex optimization | Convex functions | embedded control | operator splitting | Fixed-point arithmetic | Predictive control | optimal control | ACTIVE-SET | MPC | ENGINEERING, ELECTRICAL & ELECTRONIC | SYSTEMS | ROBUST OPTIMAL-CONTROL | AUTOMATION & CONTROL SYSTEMS | Splitting | Algorithms | Mathematical analysis | Control systems | Field programmable gate arrays | Optimization | Arithmetic

Algorithm design and analysis | Matrix decomposition | Sparse matrices | fixed point algorithms for control | model predictive control (MPC) | Alternating directions method of multipliers (ADMM) | Optimal control | convex optimization | Convex functions | embedded control | operator splitting | Fixed-point arithmetic | Predictive control | optimal control | ACTIVE-SET | MPC | ENGINEERING, ELECTRICAL & ELECTRONIC | SYSTEMS | ROBUST OPTIMAL-CONTROL | AUTOMATION & CONTROL SYSTEMS | Splitting | Algorithms | Mathematical analysis | Control systems | Field programmable gate arrays | Optimization | Arithmetic

Journal Article

01/2017, Scientific Computation, ISBN 3319415875, 822

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors...

Physics | Mathematical optimization | Computational Mathematics and Numerical Analysis | Mathematics | Numerical and Computational Physics, Simulation | Optimization | Image Processing and Computer Vision

Physics | Mathematical optimization | Computational Mathematics and Numerical Analysis | Mathematics | Numerical and Computational Physics, Simulation | Optimization | Image Processing and Computer Vision

eBook

Mathematical programming, ISSN 1436-4646, 2019, Volume 182, Issue 1-2, pp. 233 - 273

Journal Article

Advances in computational mathematics, ISSN 1572-9044, 2011, Volume 38, Issue 3, pp. 667 - 681

.... Several splitting algorithms recently proposed in the literature are recovered as special cases.

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | MATHEMATICS, APPLIED | DECOMPOSITION | CONVEX MINIMIZATION PROBLEMS | VARIATIONAL-INEQUALITIES | CONVERGENCE | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | MATHEMATICS, APPLIED | DECOMPOSITION | CONVEX MINIMIZATION PROBLEMS | VARIATIONAL-INEQUALITIES | CONVERGENCE | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

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

SIAM journal on optimization, ISSN 1095-7189, 2011, Volume 21, Issue 4, pp. 1230 - 1250

.... New primal-dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators, and convergence results are established...

Monotone inclusion | Minimization algorithm | Convex optimization | Composite operator | Operator splitting | Decomposition | Duality | Fenchel-Rockafellar duality | Monotone operator | Forward-backward-forward algorithm | Mathematics | Optimization and Control

Monotone inclusion | Minimization algorithm | Convex optimization | Composite operator | Operator splitting | Decomposition | Duality | Fenchel-Rockafellar duality | Monotone operator | Forward-backward-forward algorithm | Mathematics | Optimization and Control

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 6/2018, Volume 2018, Issue 6, pp. 1 - 38

We consider the expansion of small-x resummed DGLAP splitting functions at next-to-leading logarithmic (NLL...

Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | QCD Phenomenology | Elementary Particles, Quantum Field Theory | RESUMMATION | HIGH-ENERGY FACTORIZATION | OPERATOR MATRIX-ELEMENTS | QCD | SINGULARITY | DEEP-INELASTIC SCATTERING | WILSON COEFFICIENTS | PHYSICS, PARTICLES & FIELDS | Employee motivation | Splitting | Physics - High Energy Physics - Phenomenology | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology

Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | QCD Phenomenology | Elementary Particles, Quantum Field Theory | RESUMMATION | HIGH-ENERGY FACTORIZATION | OPERATOR MATRIX-ELEMENTS | QCD | SINGULARITY | DEEP-INELASTIC SCATTERING | WILSON COEFFICIENTS | PHYSICS, PARTICLES & FIELDS | Employee motivation | Splitting | Physics - High Energy Physics - Phenomenology | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Phenomenology

Journal Article

Multiscale modeling & simulation, ISSN 1540-3467, 2005, Volume 4, Issue 4, pp. 1168 - 1200

.... Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem...

Proximal Landweber method | Proximity operator | Image decomposition | Iterative soft-thresholding | Signal recovery | Image restoration | Forward-backward algorithm | Multiresolution analysis | Denoising | Inverse problem | inverse problem | forward-backward algorithm | RECONSTRUCTION | ALGORITHM | signal recovery | RESTORATION | PHYSICS, MATHEMATICAL | LEAST-SQUARES | denoising | PROJECTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | image restoration | LINEAR INVERSE PROBLEMS | iterative soft-thresholding | ANALYSE FONCTIONNELLE | proximity operator | proximal Landweber method | multiresolution analysis | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | image decomposition

Proximal Landweber method | Proximity operator | Image decomposition | Iterative soft-thresholding | Signal recovery | Image restoration | Forward-backward algorithm | Multiresolution analysis | Denoising | Inverse problem | inverse problem | forward-backward algorithm | RECONSTRUCTION | ALGORITHM | signal recovery | RESTORATION | PHYSICS, MATHEMATICAL | LEAST-SQUARES | denoising | PROJECTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | image restoration | LINEAR INVERSE PROBLEMS | iterative soft-thresholding | ANALYSE FONCTIONNELLE | proximity operator | proximal Landweber method | multiresolution analysis | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | image decomposition

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 9/2017, Volume 68, Issue 1, pp. 57 - 93

In this work we propose a new splitting technique, namely Asymmetric Forward–Backward–Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator...

Monotone inclusion | Primal-dual algorithms | Convex optimization | Convex and Discrete Geometry | Operator splitting | Mathematics | Operations Research, Management Science | Operation Research/Decision Theory | Statistics, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Electrical engineering | Algorithms | Computational geometry | Splitting | Asymmetry | Convexity | Inclusions | Preconditioning

Monotone inclusion | Primal-dual algorithms | Convex optimization | Convex and Discrete Geometry | Operator splitting | Mathematics | Operations Research, Management Science | Operation Research/Decision Theory | Statistics, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Electrical engineering | Algorithms | Computational geometry | Splitting | Asymmetry | Convexity | Inclusions | Preconditioning

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2016, Volume 276, pp. 454 - 467

We derive an analytical approach to the Strang splitting method for the Burgers–Huxley equation (BHE) ut+αuux−ϵuxx=β(1−u)(u−γ)u. We proved that Srtang splitting method has a second order convergence in Hs...

Error analysis | Burgers–Huxley equation | Sobolev spaces | Regularity | Operator splitting method | Burgers-Huxley equation | MATHEMATICS, APPLIED | Soholev spaces | Sects | Methods | Integers | Splitting | Computation | Sobolev space | Mathematical analysis | Mathematical models | Convergence

Error analysis | Burgers–Huxley equation | Sobolev spaces | Regularity | Operator splitting method | Burgers-Huxley equation | MATHEMATICS, APPLIED | Soholev spaces | Sects | Methods | Integers | Splitting | Computation | Sobolev space | Mathematical analysis | Mathematical models | Convergence

Journal Article