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

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

We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators...

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

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

Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 183, Issue 1, pp. 179 - 198

The Douglas–Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper, closed, and convex functions and, more generally, two maximally monotone operators...

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglas–Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglas–Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Journal Article

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

... individually via their proximity operators. This work brings together and notably extends several classical splitting schemes, like the forward...

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

Set-Valued and Variational Analysis, ISSN 1877-0533, 12/2017, Volume 25, Issue 4, pp. 829 - 858

Operator-splitting methods convert optimization and inclusion problems into fixed-point equations...

Monotone inclusion | 65K15 | 65K05 | Three operators | Probability Theory and Stochastic Processes | Mathematics | Forward backward | Convex optimization | 90C25 | Analysis | Operator splitting | Acceleration | Douglas Rachford | 47H05 | Fixed point | MATHEMATICS, APPLIED | INCLUSIONS | CONVERGENCE RATE ANALYSIS | SUM | ALGORITHMS

Monotone inclusion | 65K15 | 65K05 | Three operators | Probability Theory and Stochastic Processes | Mathematics | Forward backward | Convex optimization | 90C25 | Analysis | Operator splitting | Acceleration | Douglas Rachford | 47H05 | Fixed point | MATHEMATICS, APPLIED | INCLUSIONS | CONVERGENCE RATE ANALYSIS | SUM | ALGORITHMS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 15

In this paper, we investigate a splitting algorithm for treating monotone operators...

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | APPROXIMATION | ITERATIVE ALGORITHM | MATHEMATICS | SEMIGROUPS | THEOREMS | MAPPINGS | ZERO POINTS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | APPROXIMATION | ITERATIVE ALGORITHM | MATHEMATICS | SEMIGROUPS | THEOREMS | MAPPINGS | ZERO POINTS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

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

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

Computational optimization and applications, ISSN 1573-2894, 2018, Volume 70, Issue 3, pp. 763 - 790

This paper considers the relaxed Peaceman–Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators...

Relaxed Peaceman–Rachford splitting method | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | Strongly monotone operators | Non-Euclidean hybrid proximal extragradient framework | EXTRAGRADIENT | RATES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | PROXIMAL POINT ALGORITHM | SUBSPACES | Relaxed Peaceman-Rachford splitting method | SADDLE-POINT | LINEAR CONVERGENCE | Operators | Splitting | Parameters | Convergence

Relaxed Peaceman–Rachford splitting method | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | Strongly monotone operators | Non-Euclidean hybrid proximal extragradient framework | EXTRAGRADIENT | RATES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | PROXIMAL POINT ALGORITHM | SUBSPACES | Relaxed Peaceman-Rachford splitting method | SADDLE-POINT | LINEAR CONVERGENCE | Operators | Splitting | Parameters | Convergence

Journal Article

Journal of approximation theory, ISSN 0021-9045, 2012, Volume 164, Issue 8, pp. 1065 - 1084

The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis...

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2017, Volume 175, Issue 3, pp. 818 - 847

... by Monteiro and Svaiter. As applications, we propose and analyze the iteration-complexity of an inexact operator splitting algorithm...

Iteration-complexity | Composite optimization | Forward–backward | Mathematics | Theory of Computation | Inexact proximal point methods | Parallel | Optimization | Splitting | 47J20 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Partial inverse method | 90C33 | 90C060 | 65K10 | Applications of Mathematics | Engineering, general | 47H05 | Forward-backward | MATHEMATICS, APPLIED | ENLARGEMENT | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPLEXITY | MONOTONE-OPERATORS | Methods | Algorithms | Computational geometry | Convexity | Complexity | Inverse method

Iteration-complexity | Composite optimization | Forward–backward | Mathematics | Theory of Computation | Inexact proximal point methods | Parallel | Optimization | Splitting | 47J20 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Partial inverse method | 90C33 | 90C060 | 65K10 | Applications of Mathematics | Engineering, general | 47H05 | Forward-backward | MATHEMATICS, APPLIED | ENLARGEMENT | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPLEXITY | MONOTONE-OPERATORS | Methods | Algorithms | Computational geometry | Convexity | Complexity | Inverse method

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 2011, Volume 20, Issue 2, pp. 307 - 330

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators...

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | MATHEMATICS, APPLIED | STABILITY | DECOMPOSITION | PROXIMAL POINT ALGORITHM | VARIATIONAL-INEQUALITIES | RECOVERY | MINIMIZATION | MAPPINGS | Algorithms | Optimization and Control

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | MATHEMATICS, APPLIED | STABILITY | DECOMPOSITION | PROXIMAL POINT ALGORITHM | VARIATIONAL-INEQUALITIES | RECOVERY | MINIMIZATION | MAPPINGS | Algorithms | Optimization and Control

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

Symmetry (Basel), ISSN 2073-8994, 2018, Volume 10, Issue 11, p. 563

The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive...

Inexact three-operator splitting algorithm | Nonexpansive operator | Fixed point | RECOVERY | fixed point | MULTIDISCIPLINARY SCIENCES | PROXIMAL POINT ALGORITHM | OPTIMIZATION | inexact three-operator splitting algorithm | nonexpansive operator | SOLVING MONOTONE INCLUSIONS

Inexact three-operator splitting algorithm | Nonexpansive operator | Fixed point | RECOVERY | fixed point | MULTIDISCIPLINARY SCIENCES | PROXIMAL POINT ALGORITHM | OPTIMIZATION | inexact three-operator splitting algorithm | nonexpansive operator | SOLVING MONOTONE INCLUSIONS

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 178, Issue 1, pp. 153 - 190

In this work, we study the pointwise and ergodic iteration complexity of a family of projective splitting methods proposed by Eckstein and Svaiter, for finding a zero of the sum of two maximal monotone operators...

Maximal monotone operators | 65K05 | Splitting algorithms | Mathematics | Theory of Computation | Optimization | Complexity | Spingarn’s method | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 49M27 | Applications of Mathematics | Engineering, general | 47H05 | 90C60 | EXTRAGRADIENT | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Spingarn's method | ENLARGEMENT | PROXIMAL POINT ALGORITHM | HILBERT-SPACE | Analysis | Methods | Algorithms | Operators | Splitting | Inverse method

Maximal monotone operators | 65K05 | Splitting algorithms | Mathematics | Theory of Computation | Optimization | Complexity | Spingarn’s method | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 49M27 | Applications of Mathematics | Engineering, general | 47H05 | 90C60 | EXTRAGRADIENT | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Spingarn's method | ENLARGEMENT | PROXIMAL POINT ALGORITHM | HILBERT-SPACE | Analysis | Methods | Algorithms | Operators | Splitting | Inverse method

Journal Article

Optimization, ISSN 0233-1934, 09/2014, Volume 63, Issue 9, pp. 1289 - 1318

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces...

quasi-Fejér sequence | cocoercive operator | primal-dual algorithm | forward-backward splitting algorithm | composite operator | demiregularity | duality | monotone inclusion | variable metric | monotone operator | MATHEMATICS, APPLIED | SIGNAL RECOVERY | ALGORITHM | DECOMPOSITION | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | quasi-Fejer sequence | NONDIFFERENTIABLE CONVEX-OPTIMIZATION | CONVERGENCE | DUALIZATION | Mathematics | Optimization and Control

quasi-Fejér sequence | cocoercive operator | primal-dual algorithm | forward-backward splitting algorithm | composite operator | demiregularity | duality | monotone inclusion | variable metric | monotone operator | MATHEMATICS, APPLIED | SIGNAL RECOVERY | ALGORITHM | DECOMPOSITION | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | quasi-Fejer sequence | NONDIFFERENTIABLE CONVEX-OPTIMIZATION | CONVERGENCE | DUALIZATION | Mathematics | Optimization and Control

Journal Article

Mathematical Programming, ISSN 0025-5610, 2015, Volume 150, Issue 2, pp. 251 - 279

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in V (Adv Comput Math 38(3):667-681, 2013...

Maximally monotone operator | Resolvent | Subdifferential | Operator splitting | Convex optimization algorithm | Duality | Strongly monotone operator | Strongly convex function | MATHEMATICS, APPLIED | COMPOSITE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | OPERATORS | Algorithms | Image processing | Mathematical optimization | Analysis | Studies | Optimization algorithms | Mathematical analysis | Operators | Splitting | Texts | Pattern recognition | Inclusions | Optimization | Convergence

Maximally monotone operator | Resolvent | Subdifferential | Operator splitting | Convex optimization algorithm | Duality | Strongly monotone operator | Strongly convex function | MATHEMATICS, APPLIED | COMPOSITE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | OPERATORS | Algorithms | Image processing | Mathematical optimization | Analysis | Studies | Optimization algorithms | Mathematical analysis | Operators | Splitting | Texts | Pattern recognition | Inclusions | Optimization | Convergence

Journal Article