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

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

In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces...

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

Numerical algorithms, ISSN 1572-9265, 2015, Volume 71, Issue 3, pp. 519 - 540

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator...

Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | COMPOSITE | CONVERGENCE | MAPPINGS | OPTIMIZATION | OPERATORS | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence

Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | COMPOSITE | CONVERGENCE | MAPPINGS | OPTIMIZATION | OPERATORS | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence

Journal Article

Optimization, ISSN 0233-1934, 06/2016, Volume 65, Issue 6, pp. 1293 - 1314

We propose an inertial forward-backward splitting algorithm to compute a zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators...

Monotone inclusion | cocoercive operator | forward-backward algorithm | primal-dual algorithm | composite operator | operator splitting | duality | monotone operator | forward–backward algorithm | primal–dual algorithm | SPARSITY | MATHEMATICS, APPLIED | DECOMPOSITION | PROXIMAL METHODS | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | REGULARIZATION | OPERATORS | Algorithms | Stochastic models | Operators | Splitting | Stochasticity | Inertial | Inclusions | Optimization | Convergence

Monotone inclusion | cocoercive operator | forward-backward algorithm | primal-dual algorithm | composite operator | operator splitting | duality | monotone operator | forward–backward algorithm | primal–dual algorithm | SPARSITY | MATHEMATICS, APPLIED | DECOMPOSITION | PROXIMAL METHODS | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | REGULARIZATION | OPERATORS | Algorithms | Stochastic models | Operators | Splitting | Stochasticity | Inertial | Inclusions | Optimization | Convergence

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 179, Issue 1, pp. 1 - 36

...–backward algorithms in the presence of perturbations, approximations, errors. These splitting algorithms aim to solve, by rapid methods, structured convex minimization problems...

FISTA | 65K05 | Mathematics | Theory of Computation | Tikhonov regularization | Optimization | Accelerated Nesterov method | Inertial forward–backward algorithms | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | Perturbations | Structured convex optimization | MATHEMATICS, APPLIED | STABILIZATION | PROXIMAL POINT ALGORITHM | VISCOSITY | SPLITTING METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | DYNAMICS | CONVERGENCE | Inertial forward-backward algorithms | MONOTONE-OPERATORS | Algorithms | Extrapolation | Approximation | Hilbert space | Coefficients | Regularization | Convergence | Optimization and Control

FISTA | 65K05 | Mathematics | Theory of Computation | Tikhonov regularization | Optimization | Accelerated Nesterov method | Inertial forward–backward algorithms | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | Perturbations | Structured convex optimization | MATHEMATICS, APPLIED | STABILIZATION | PROXIMAL POINT ALGORITHM | VISCOSITY | SPLITTING METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | DYNAMICS | CONVERGENCE | Inertial forward-backward algorithms | MONOTONE-OPERATORS | Algorithms | Extrapolation | Approximation | Hilbert space | Coefficients | Regularization | Convergence | Optimization and Control

Journal Article

SIAM journal on optimization, ISSN 1095-7189, 2015, Volume 25, Issue 4, pp. 2120 - 2142

In this paper, we first propose a general inertial proximal point algorithm (PPA) for the mixed variational inequality...

Inertial linearized alternating direction method of multipliers | Mixed variational inequality | Inertial linearized augmented lagrangian method | Inertial proximal point algorithm | SYSTEM | MATHEMATICS, APPLIED | DISCRETIZATION | MAXIMAL MONOTONE-OPERATORS | inertial linearized alternating direction method of multipliers | CONVERGENCE | FORWARD-BACKWARD ALGORITHM | inertial proximal point algorithm | inertial linearized augmented Lagrangian method | SPLITTING METHOD | mixed variational inequality

Inertial linearized alternating direction method of multipliers | Mixed variational inequality | Inertial linearized augmented lagrangian method | Inertial proximal point algorithm | SYSTEM | MATHEMATICS, APPLIED | DISCRETIZATION | MAXIMAL MONOTONE-OPERATORS | inertial linearized alternating direction method of multipliers | CONVERGENCE | FORWARD-BACKWARD ALGORITHM | inertial proximal point algorithm | inertial linearized augmented Lagrangian method | SPLITTING METHOD | mixed variational inequality

Journal Article

Numerical functional analysis and optimization, ISSN 1532-2467, 2015, Volume 36, Issue 8, pp. 951 - 963

In this article, we incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed to find the zeros...

Enlargement of a maximally monotone operator | Maximally monotone operator | Resolvent | Hybrid proximal point algorithm | Inertial splitting algorithm | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | CONVERGENCE | ENLARGEMENT | POINT ALGORITHM | Operators (mathematics) | Algorithms | Mathematical models | Functional analysis | Inertial | Iterative methods | Optimization | Convergence

Enlargement of a maximally monotone operator | Maximally monotone operator | Resolvent | Hybrid proximal point algorithm | Inertial splitting algorithm | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | CONVERGENCE | ENLARGEMENT | POINT ALGORITHM | Operators (mathematics) | Algorithms | Mathematical models | Functional analysis | Inertial | Iterative methods | Optimization | Convergence

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2017, Volume 27, Issue 4, pp. 2356 - 2380

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms...

Proximal algorithm | Fixed point iteration | Monotone operator splitting | Nonsmooth minimization | Averaged operator | Mean value iterations | Forward-backward algorithm | Inertial algorithm | Peaceman–Rachford algorithm | SYSTEM | MATHEMATICS, APPLIED | forward-backward algorithm | MAXIMAL MONOTONE-OPERATORS | fixed point iteration | monotone operator splitting | mean value iterations | FIXED-POINT ITERATIONS | Peaceman-Rachford algorithm | nonsmooth minimization | averaged operator | proximal algorithm | CONVERGENCE | inertial algorithm | Mathematics

Proximal algorithm | Fixed point iteration | Monotone operator splitting | Nonsmooth minimization | Averaged operator | Mean value iterations | Forward-backward algorithm | Inertial algorithm | Peaceman–Rachford algorithm | SYSTEM | MATHEMATICS, APPLIED | forward-backward algorithm | MAXIMAL MONOTONE-OPERATORS | fixed point iteration | monotone operator splitting | mean value iterations | FIXED-POINT ITERATIONS | Peaceman-Rachford algorithm | nonsmooth minimization | averaged operator | proximal algorithm | CONVERGENCE | inertial algorithm | Mathematics

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 06/2017, Volume 67, Issue 2, pp. 259 - 292

.... We analyze a family of generalized inertial proximal splitting algorithms (GIPSA) for solving such problems...

FISTA | Inertial forward-backward splitting | Inertial proximal gradient | Local linear convergence | Momentum methods | Lasso | MATHEMATICS, APPLIED | GRADIENT METHODS | ALGORITHMS | LINEAR CONVERGENCE | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MONOTONE-OPERATORS | Studies | Problem solving | Theorems | Mathematical models | Mathematics | Optimization | Manifolds | Splitting | Algorithms | Mathematical analysis | Iterative methods | Convergence

FISTA | Inertial forward-backward splitting | Inertial proximal gradient | Local linear convergence | Momentum methods | Lasso | MATHEMATICS, APPLIED | GRADIENT METHODS | ALGORITHMS | LINEAR CONVERGENCE | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MONOTONE-OPERATORS | Studies | Problem solving | Theorems | Mathematical models | Mathematics | Optimization | Manifolds | Splitting | Algorithms | Mathematical analysis | Iterative methods | Convergence

Journal Article

International journal of computer mathematics, ISSN 1029-0265, 2019, Volume 97, Issue 1-2, pp. 482 - 497

In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward-backward splitting algorithm...

forward-backward algorithm | monotone inclusion problems | Inertial algorithm | inertial splitting algorithm | MATHEMATICS, APPLIED | PROXIMAL METHOD | CONVERGENCE | Splitting | Hilbert space | Algorithms | Image restoration | Inclusions

forward-backward algorithm | monotone inclusion problems | Inertial algorithm | inertial splitting algorithm | MATHEMATICS, APPLIED | PROXIMAL METHOD | CONVERGENCE | Splitting | Hilbert space | Algorithms | Image restoration | Inclusions

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2015, Volume 166, Issue 3, pp. 968 - 982

We discuss here the convergence of the iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm...

Forward backward splitting | Inertial algorithms | Mathematics | Theory of Computation | 65Y20 | Optimization | Convergence | 65B99 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | First-order schemes | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | INERTIAL PROXIMAL METHOD | Algorithms | Studies | Optimization algorithms | Hilbert space | Euclidean space | Mathematical analysis | Construction | Euclidean geometry | Inverse | Shrinkage | Iterative methods

Forward backward splitting | Inertial algorithms | Mathematics | Theory of Computation | 65Y20 | Optimization | Convergence | 65B99 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | First-order schemes | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | INERTIAL PROXIMAL METHOD | Algorithms | Studies | Optimization algorithms | Hilbert space | Euclidean space | Mathematical analysis | Construction | Euclidean geometry | Inverse | Shrinkage | Iterative methods

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2018, Volume 20, Issue 1, pp. 1 - 17

.... For solving this problem, we propose an inertial forward–backward splitting algorithm involving an extrapolation factor...

maximal monotone operator | Mathematical Methods in Physics | 47H10 | Analysis | inclusion problem | forward–backward algorithm | Mathematics, general | Mathematics | Inertial method | Hilbert space | 47H04 | MATHEMATICS, APPLIED | forward-backward algorithm | APPROXIMATION | FEASIBILITY PROBLEM | EQUATIONS | PROXIMAL POINT ALGORITHM | SUM | MATHEMATICS | RESOLVENTS | EQUILIBRIA | CONVERGENCE | MAPPINGS | MONOTONE-OPERATORS | Methods | Algorithms

maximal monotone operator | Mathematical Methods in Physics | 47H10 | Analysis | inclusion problem | forward–backward algorithm | Mathematics, general | Mathematics | Inertial method | Hilbert space | 47H04 | MATHEMATICS, APPLIED | forward-backward algorithm | APPROXIMATION | FEASIBILITY PROBLEM | EQUATIONS | PROXIMAL POINT ALGORITHM | SUM | MATHEMATICS | RESOLVENTS | EQUILIBRIA | CONVERGENCE | MAPPINGS | MONOTONE-OPERATORS | Methods | Algorithms

Journal Article

SIAM journal on optimization, ISSN 1052-6234, 2020, Volume 30, Issue 2, pp. 1451 - 1472

In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators...

MATHEMATICS, APPLIED | GRADIENT METHODS | forward-backward algorithm | SEARCH | INERTIAL PROXIMAL METHOD | ALGORITHM | CONVERGENCE | SUM | Tseng's method | operator splitting | OPERATORS

MATHEMATICS, APPLIED | GRADIENT METHODS | forward-backward algorithm | SEARCH | INERTIAL PROXIMAL METHOD | ALGORITHM | CONVERGENCE | SUM | Tseng's method | operator splitting | OPERATORS

Journal Article

SIAM Journal on Imaging Sciences, ISSN 1936-4954, 06/2014, Volume 7, Issue 2, pp. 1388 - 1419

... (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force...

Heavy-ball method | Inertial forward-backward splitting | Proof of convergence | Nonconvex optimization | Kurdyka-lojasiewicz inequality | inertial forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | CONVERGENCE ANALYSIS | MAXIMAL MONOTONE-OPERATORS | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | nonconvex optimization | COMPRESSION | proof of convergence | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PRIMAL-DUAL ALGORITHMS | MINIMIZATION | POINT ALGORITHM | Theorems | Algorithms | Mathematical analysis | Mathematical models | Image compression | Inertial | Optimization | Convergence

Heavy-ball method | Inertial forward-backward splitting | Proof of convergence | Nonconvex optimization | Kurdyka-lojasiewicz inequality | inertial forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | CONVERGENCE ANALYSIS | MAXIMAL MONOTONE-OPERATORS | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | nonconvex optimization | COMPRESSION | proof of convergence | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PRIMAL-DUAL ALGORITHMS | MINIMIZATION | POINT ALGORITHM | Theorems | Algorithms | Mathematical analysis | Mathematical models | Image compression | Inertial | Optimization | Convergence

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2020, Volume 75, Issue 2, pp. 389 - 422

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM...

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | Convex optimization | Douglas-Rachford splitting | SHRINKAGE | Inertial algorithms | WEAK-CONVERGENCE | PROXIMAL POINT ALGORITHM | ADMM | Computational geometry | Splitting | Algorithms | Regression analysis | Convexity | Optimization

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | Convex optimization | Douglas-Rachford splitting | SHRINKAGE | Inertial algorithms | WEAK-CONVERGENCE | PROXIMAL POINT ALGORITHM | ADMM | Computational geometry | Splitting | Algorithms | Regression analysis | Convexity | Optimization

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 177, Issue 1, pp. 153 - 180

...) minimum, stays in its neighborhood, and converges within this neighborhood. This result allows algorithms to exploit local properties of the objective function...

Alternating projection | 65K05 | iPiano | Mathematics | Theory of Computation | Non-convex feasibility | 90C26 | Optimization | Prox-regularity | Gradient of Moreau envelopes | Averaged projection | 90C30 | Inertial forward–backward splitting | Calculus of Variations and Optimal Control; Optimization | 49J52 | Operations Research/Decision Theory | Heavy-ball method | Applications of Mathematics | Engineering, general | POLYNOMIAL SYSTEMS | MATHEMATICS, APPLIED | STABILITY | PROXIMAL ALGORITHM | Inertial forward-backward splitting | DESCENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONSMOOTH | ERROR-BOUNDS | ALTERNATING LINEARIZED MINIMIZATION | Algorithms | Mathematical optimization | Analysis | Methods | Computational geometry | Neighborhoods | Convexity | Equivalence | Convergence

Alternating projection | 65K05 | iPiano | Mathematics | Theory of Computation | Non-convex feasibility | 90C26 | Optimization | Prox-regularity | Gradient of Moreau envelopes | Averaged projection | 90C30 | Inertial forward–backward splitting | Calculus of Variations and Optimal Control; Optimization | 49J52 | Operations Research/Decision Theory | Heavy-ball method | Applications of Mathematics | Engineering, general | POLYNOMIAL SYSTEMS | MATHEMATICS, APPLIED | STABILITY | PROXIMAL ALGORITHM | Inertial forward-backward splitting | DESCENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONSMOOTH | ERROR-BOUNDS | ALTERNATING LINEARIZED MINIMIZATION | Algorithms | Mathematical optimization | Analysis | Methods | Computational geometry | Neighborhoods | Convexity | Equivalence | Convergence

Journal Article

Minimax Theory and its Applications, ISSN 2199-1413, 2016, Volume 1, Issue 1, pp. 29 - 49

Journal Article

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, 04/2019, Volume 113, Issue 2, pp. 645 - 656

In this paper, we propose a modified forward-backward splitting method using the shrinking projection and the inertial technique for solving the inclusion problem of the sum of two monotone operators...

Shrinking projection method | MATHEMATICS | 47H10 | Inertial method | Maximal monotone operator | Inclusion problem | Forward-backward algorithm | 47H04

Shrinking projection method | MATHEMATICS | 47H10 | Inertial method | Maximal monotone operator | Inclusion problem | Forward-backward algorithm | 47H04

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2020, Volume 374, p. 112772

We consider an inertial proximal strictly contractive Peaceman–Rachford splitting method...

Indefinite | Peaceman–Rachford splitting method | Global convergence | Inertial proximal point | Variational inequality | Convex programming | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | Peaceman-Rachford splitting method | MULTIPLIERS | ALTERNATING DIRECTION METHOD | MINIMIZATION | SHRINKAGE | WEAK-CONVERGENCE | POINT ALGORITHM

Indefinite | Peaceman–Rachford splitting method | Global convergence | Inertial proximal point | Variational inequality | Convex programming | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | Peaceman-Rachford splitting method | MULTIPLIERS | ALTERNATING DIRECTION METHOD | MINIMIZATION | SHRINKAGE | WEAK-CONVERGENCE | POINT ALGORITHM

Journal Article

20.
Full Text
A Dynamical Approach to an Inertial Forward-Backward Algorithm for Convex Minimization

SIAM journal on optimization, ISSN 1095