Mathematical programming, ISSN 1436-4646, 2011, Volume 137, Issue 1-2, pp. 91 - 129

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance...

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | POINT ALGORITHM | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | POINT ALGORITHM | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Journal Article

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

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

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 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

SIAM journal on imaging sciences, ISSN 1936-4954, 2015, Volume 8, Issue 1, pp. 644 - 681

We present a novel framework, namely, accelerated alternating direction method of multipliers (AADMM...

Alternating direction method of multipliers | Accelerated gradient method | Convex optimization | MATHEMATICS, APPLIED | accelerated gradient method | PENALTY SCHEMES | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | PROXIMAL POINT ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATION IMAGE-RECONSTRUCTION | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PRIMAL-DUAL ALGORITHMS | ITERATION-COMPLEXITY | alternating direction method of multipliers | convex optimization | FORWARD-BACKWARD | SADDLE-POINT | MONOTONE-OPERATORS | Multipliers | Algorithms | Saddle points | Imaging | Constants | Acceleration | Optimization | Convergence

Alternating direction method of multipliers | Accelerated gradient method | Convex optimization | MATHEMATICS, APPLIED | accelerated gradient method | PENALTY SCHEMES | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | PROXIMAL POINT ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATION IMAGE-RECONSTRUCTION | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PRIMAL-DUAL ALGORITHMS | ITERATION-COMPLEXITY | alternating direction method of multipliers | convex optimization | FORWARD-BACKWARD | SADDLE-POINT | MONOTONE-OPERATORS | Multipliers | Algorithms | Saddle points | Imaging | Constants | Acceleration | Optimization | Convergence

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

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2018, Volume 176, Issue 1, pp. 137 - 162

We consider the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under the Kurdyka...

Forward–Backward splitting | 65K05 | Mathematics | Theory of Computation | Optimization | Extragradient | 90C30 | 90C52 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Descent method | Applications of Mathematics | Engineering, general | Complexity, first-order method | 49M37 | LASSO problem | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | SHRINKAGE | ALGORITHM | DESCENT METHODS | Forward-Backward splitting | Critical point | Methods | Convergence | Complexity | Optimization and Control

Forward–Backward splitting | 65K05 | Mathematics | Theory of Computation | Optimization | Extragradient | 90C30 | 90C52 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Descent method | Applications of Mathematics | Engineering, general | Complexity, first-order method | 49M37 | LASSO problem | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | SHRINKAGE | ALGORITHM | DESCENT METHODS | Forward-Backward splitting | Critical point | Methods | Convergence | Complexity | Optimization and Control

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 4, pp. A2558 - A2584

Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one, and their investigation has comprised...

Forward-backward inertial methods | Probability density estimation | Signal restoration | Convex optimization | MATHEMATICS, APPLIED | GRADIENT METHODS | signal restoration | ALGORITHM | convex optimization | forward-backward inertial methods | RESTORATION | probability density estimation

Forward-backward inertial methods | Probability density estimation | Signal restoration | Convex optimization | MATHEMATICS, APPLIED | GRADIENT METHODS | signal restoration | ALGORITHM | convex optimization | forward-backward inertial methods | RESTORATION | probability density estimation

Journal Article

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

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial 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

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

SIAM journal on control and optimization, ISSN 1095-7138, 2000, Volume 38, Issue 2, pp. 431 - 446

We consider the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings...

MATHEMATICS, APPLIED | DECOMPOSITION METHOD | VARIATIONAL INEQUALITY PROBLEM | EQUATIONS | convex programming | variational inequality | decomposition | PROXIMAL POINT ALGORITHM | SUM | CONVEX MINIMIZATION PROBLEMS | maximal monotone mapping | extragradient method | CONVERGENCE | ITERATIVE METHODS | forward-backward splitting method | OPERATORS | AUTOMATION & CONTROL SYSTEMS

MATHEMATICS, APPLIED | DECOMPOSITION METHOD | VARIATIONAL INEQUALITY PROBLEM | EQUATIONS | convex programming | variational inequality | decomposition | PROXIMAL POINT ALGORITHM | SUM | CONVEX MINIMIZATION PROBLEMS | maximal monotone mapping | extragradient method | CONVERGENCE | ITERATIVE METHODS | forward-backward splitting method | OPERATORS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Calcolo, ISSN 1126-5434, 2018, Volume 56, Issue 1, pp. 1 - 21

Strong convergence property for Halpern-type iterative method with inertial terms for solving variational inequalities in real Hilbert spaces is investigated under mild assumptions in this paper...

Strong convergence | 65K15 | Hilbert spaces | Mathematics | Theory of Computation | Monotone operator | Inertial terms | 47J20 | 90C25 | Numerical Analysis | 47H05 | 47J25 | Variational inequalities | PROXIMAL POINT | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT METHODS | MAXIMAL MONOTONE-OPERATORS | HYBRID METHOD | STEP | MATHEMATICS | COMMON FIXED-POINTS | SUBGRADIENT EXTRAGRADIENT METHOD | FORWARD-BACKWARD ALGORITHM | STRONG-CONVERGENCE | Mathematical analysis | Inequalities | Control systems | Hilbert space | Iterative methods | Estimates | Cybernetics | Convergence

Strong convergence | 65K15 | Hilbert spaces | Mathematics | Theory of Computation | Monotone operator | Inertial terms | 47J20 | 90C25 | Numerical Analysis | 47H05 | 47J25 | Variational inequalities | PROXIMAL POINT | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT METHODS | MAXIMAL MONOTONE-OPERATORS | HYBRID METHOD | STEP | MATHEMATICS | COMMON FIXED-POINTS | SUBGRADIENT EXTRAGRADIENT METHOD | FORWARD-BACKWARD ALGORITHM | STRONG-CONVERGENCE | Mathematical analysis | Inequalities | Control systems | Hilbert space | Iterative methods | Estimates | Cybernetics | Convergence

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2009, Volume 48, Issue 5, pp. 3246 - 3270

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist...

Evolution inclusion | Weak convergence | Coupled systems | Parallel algorithm | Operator splitting | Maximal monotone operator | Demiregular operator | Forward-backward algorithm | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | evolution inclusion | forward-backward algorithm | APPROXIMATION | demiregular operator | parallel algorithm | ALGORITHMS | PROJECTION METHODS | coupled systems | maximal monotone operator | VARIATIONAL-INEQUALITIES | CONSTRUCTION | CONVERGENCE | MAPPINGS | weak convergence | HILBERT-SPACE | operator splitting | OPERATORS | AUTOMATION & CONTROL SYSTEMS | Studies | Nonlinear programming | Approximations | Convergence

Evolution inclusion | Weak convergence | Coupled systems | Parallel algorithm | Operator splitting | Maximal monotone operator | Demiregular operator | Forward-backward algorithm | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | evolution inclusion | forward-backward algorithm | APPROXIMATION | demiregular operator | parallel algorithm | ALGORITHMS | PROJECTION METHODS | coupled systems | maximal monotone operator | VARIATIONAL-INEQUALITIES | CONSTRUCTION | CONVERGENCE | MAPPINGS | weak convergence | HILBERT-SPACE | operator splitting | OPERATORS | AUTOMATION & CONTROL SYSTEMS | Studies | Nonlinear programming | Approximations | Convergence

Journal Article

14.
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Forward–Backward Splitting Method for Solving a System of Quasi-Variational Inclusions

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 2169 - 2189

The purpose of this paper is by using a generalized forward–backward splitting method to propose an iterative algorithm for finding a common element of the set...

47H10 | Strictly pseudo-contractive mapping | 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | Forward–backward splitting algorithm | Accretive operator | Maximal-accretive operator | MATHEMATICS | Forward-backward splitting algorithm | INEQUALITY PROBLEMS | ACCRETIVE-OPERATORS | CONVERGENCE | ITERATIVE ALGORITHMS | Splitting | Iterative algorithms | Error analysis | Banach spaces | Inclusions | Banach space

47H10 | Strictly pseudo-contractive mapping | 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | Forward–backward splitting algorithm | Accretive operator | Maximal-accretive operator | MATHEMATICS | Forward-backward splitting algorithm | INEQUALITY PROBLEMS | ACCRETIVE-OPERATORS | CONVERGENCE | ITERATIVE ALGORITHMS | Splitting | Iterative algorithms | Error analysis | Banach spaces | Inclusions | Banach space

Journal Article

15.
Full Text
From error bounds to the complexity of first-order descent methods for convex functions

Mathematical programming, ISSN 1436-4646, 2016, Volume 165, Issue 2, pp. 471 - 507

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization...

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Forward-backward method | Convex minimization | Mathematical Methods in Physics | Complexity of first-order methods | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | LASSO | Error bounds | KL inequality | Combinatorics | 90C60 | Compressed sensing | POLYNOMIAL SYSTEMS | MATHEMATICS, APPLIED | INEQUALITIES | STABILITY | THRESHOLDING ALGORITHM | ASYMPTOTIC CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | OPTIMIZATION | PROJECTION ALGORITHMS | Errors | Equivalence | Globalization | Inequalities | Constants | Shrinkage | Iterative methods | Regularization | Convex analysis | Descent | Methods | Complexity

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Forward-backward method | Convex minimization | Mathematical Methods in Physics | Complexity of first-order methods | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | LASSO | Error bounds | KL inequality | Combinatorics | 90C60 | Compressed sensing | POLYNOMIAL SYSTEMS | MATHEMATICS, APPLIED | INEQUALITIES | STABILITY | THRESHOLDING ALGORITHM | ASYMPTOTIC CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | OPTIMIZATION | PROJECTION ALGORITHMS | Errors | Equivalence | Globalization | Inequalities | Constants | Shrinkage | Iterative methods | Regularization | Convex analysis | Descent | Methods | Complexity

Journal Article