Journal of Differential Equations, ISSN 0022-0396, 2015, Volume 259, Issue 7, pp. 3115 - 3143

Using small deformations of the total energy, as introduced in [31], we establish that damped second order gradient systemsu″(t)+γu′(t)+∇G(u(t))=0, may be...

Inertial systems | Global convergence | Dissipative dynamical systems | Gradient systems | Kurdyka–Łojasiewicz inequality | Kurdyka-Łojasiewicz inequality | DISSIPATION | Kurdyka-Lojasiewicz inequality | O-MINIMAL STRUCTURES | DIFFERENTIAL-EQUATION | EVOLUTION-EQUATIONS | MATHEMATICS | LONG-TIME BEHAVIOR | ANALYTIC NONLINEARITY | CONVERGENCE | BOUNDED SOLUTIONS | WAVE-EQUATION | HILBERT-SPACE | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Inertial systems | Global convergence | Dissipative dynamical systems | Gradient systems | Kurdyka–Łojasiewicz inequality | Kurdyka-Łojasiewicz inequality | DISSIPATION | Kurdyka-Lojasiewicz inequality | O-MINIMAL STRUCTURES | DIFFERENTIAL-EQUATION | EVOLUTION-EQUATIONS | MATHEMATICS | LONG-TIME BEHAVIOR | ANALYTIC NONLINEARITY | CONVERGENCE | BOUNDED SOLUTIONS | WAVE-EQUATION | HILBERT-SPACE | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

ISSN 0364-765X, 5/2010, Volume 35, Issue 2, pp. 438 - 457

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x,y)=f(x)+Q(x,y)+g(y...

alternating minimization algorithms | proximal algorithms | o-minimal structures | finite convergence time | alternating projections algorithms | gradient systems | Kurdyka- ojasiewicz inequality | nonconvex optimization | tame optimization | sparse reconstruction | convergence rate

alternating minimization algorithms | proximal algorithms | o-minimal structures | finite convergence time | alternating projections algorithms | gradient systems | Kurdyka- ojasiewicz inequality | nonconvex optimization | tame optimization | sparse reconstruction | convergence rate

Journal Article

Journal of mathematical imaging and vision, ISSN 0924-9907, 2018, Volume 61, Issue 1, pp. 122 - 139

.... The global convergence is also established. Moreover, we prove that the restorations by the algorithm have edge preservation property...

Mathematical Methods in Physics | Lower bound theory | Signal,Image and Speech Processing | Kurdyka–Łojasiewicz property | Computer Science | Image Processing and Computer Vision | Non-convex non-smooth optimization | Applications of Mathematics | Image restoration | Total variation regularization | Non-Lipschitz optimization | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | ALTERNATING MINIMIZATION | RECONSTRUCTION | SIGNALS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | MODELS | REWEIGHTED LEAST-SQUARES | CONVERGENCE | NONSMOOTH | NONCONVEX | REGULARIZATION

Mathematical Methods in Physics | Lower bound theory | Signal,Image and Speech Processing | Kurdyka–Łojasiewicz property | Computer Science | Image Processing and Computer Vision | Non-convex non-smooth optimization | Applications of Mathematics | Image restoration | Total variation regularization | Non-Lipschitz optimization | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | ALTERNATING MINIMIZATION | RECONSTRUCTION | SIGNALS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | MODELS | REWEIGHTED LEAST-SQUARES | CONVERGENCE | NONSMOOTH | NONCONVEX | REGULARIZATION

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 9/2018, Volume 18, Issue 3, pp. 1291 - 1318

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection...

Limiting subdifferential | 90C30 | Kurdyka–Łojasiewicz property | Analysis | 65K10 | Mathematics | 90C26 | 47J25 | 47H05 | Nonsmooth nonconvex optimization | 34G25 | Second-order dynamical system | MATHEMATICS | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | MAXIMAL MONOTONE-OPERATORS | INCLUSIONS | CONVERGENCE | ALGORITHMS

Limiting subdifferential | 90C30 | Kurdyka–Łojasiewicz property | Analysis | 65K10 | Mathematics | 90C26 | 47J25 | 47H05 | Nonsmooth nonconvex optimization | 34G25 | Second-order dynamical system | MATHEMATICS | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | MAXIMAL MONOTONE-OPERATORS | INCLUSIONS | CONVERGENCE | ALGORITHMS

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 04/2018, Volume 24, Issue 2, pp. 463 - 477

.... The trajectory generated by the dynamical system is proved to asymptotically converge to a critical point of the objective, provided a regularization of the latter satisfies the Kurdyka Lojasiewicz property...

Kurdyka-? ojasiewicz property | Dynamical systems | Continuous forward-backward method | Nonsmooth optimization, limiting subdifferential | continuous forward-backward method | MATHEMATICS, APPLIED | INEQUALITIES | PROXIMAL ALGORITHM | Kurdyka-Lojasiewicz property | nonsmooth optimization | limiting subdifferential | MONOTONE INCLUSIONS | CONVERGENCE | SYSTEMS | OPTIMIZATION | AUTOMATION & CONTROL SYSTEMS | Economic models | Trajectories | Critical point | Regularization | Asymptotic methods | Optimization | Convergence

Kurdyka-? ojasiewicz property | Dynamical systems | Continuous forward-backward method | Nonsmooth optimization, limiting subdifferential | continuous forward-backward method | MATHEMATICS, APPLIED | INEQUALITIES | PROXIMAL ALGORITHM | Kurdyka-Lojasiewicz property | nonsmooth optimization | limiting subdifferential | MONOTONE INCLUSIONS | CONVERGENCE | SYSTEMS | OPTIMIZATION | AUTOMATION & CONTROL SYSTEMS | Economic models | Trajectories | Critical point | Regularization | Asymptotic methods | Optimization | Convergence

Journal Article

6.
Full Text
Convergence analysis of a proximal point algorithm for minimizing differences of functions

Optimization, ISSN 0233-1934, 01/2017, Volume 66, Issue 1, pp. 129 - 147

.... We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka-ᴌojasiewicz property.

DC programming | Kurdyka-ᴌojasiewicz inequality | proximal point algorithm | difference of convex functions | Kurdyka–ᴌojasiewicz inequality | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | Kurdyka-?ojasiewicz inequality | NONCONVEX | Convex analysis | Algorithms | Convergence | Computational geometry | Numerical analysis | Mathematical analysis | Mathematical models | Convexity | Optimization

DC programming | Kurdyka-ᴌojasiewicz inequality | proximal point algorithm | difference of convex functions | Kurdyka–ᴌojasiewicz inequality | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | Kurdyka-?ojasiewicz inequality | NONCONVEX | Convex analysis | Algorithms | Convergence | Computational geometry | Numerical analysis | Mathematical analysis | Mathematical models | Convexity | Optimization

Journal Article

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, ISSN 0926-6003, 06/2019, Volume 73, Issue 2, pp. 353 - 386

Iteratively reweighted 1 algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz...

Extrapolation | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Iteratively reweighted l algorithm | Algorithms

Extrapolation | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Iteratively reweighted l algorithm | Algorithms

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2020, Volume 376, p. 112837

Iteratively reweighted algorithms are popular methods for solving nonconvex unconstrained minimization problems. Applications are notably mathematical models...

Nonsmooth objective function | Nonconvex optimization | Inexact stopping condition | Kurdyka–[formula omitted]ojasiewicz property | Iteratively reweighted algorithm | Nonconvex regularization | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | DESCENT METHODS | Kurdyka-Lojasiewicz property | INEXACT | RECOVERY | MINIMIZATION | OPTIMIZATION | NONCONVEX | POINT ALGORITHM

Nonsmooth objective function | Nonconvex optimization | Inexact stopping condition | Kurdyka–[formula omitted]ojasiewicz property | Iteratively reweighted algorithm | Nonconvex regularization | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | DESCENT METHODS | Kurdyka-Lojasiewicz property | INEXACT | RECOVERY | MINIMIZATION | OPTIMIZATION | NONCONVEX | POINT ALGORITHM

Journal Article

IEEE transaction on neural networks and learning systems, ISSN 2162-2388, 2019, Volume 30, Issue 6, pp. 1659 - 1671

.... Furthermore, based on the Kurdyka-Łojasiewicz property, we show that the sequence generated by the PLM...

Tensile stress | Computational modeling | nuclear norm | Minimization | Linear programming | Data models | proximal linearized minimization (PLM) | Numerical models | nonconvex optimization | Matrix decomposition | Kurdyka–Łojasiewicz (KL) property | tensor completion | Kurdyka-Łojasiewicz (KL) property | FACTORIZATION | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMAGE-RESTORATION | APPROXIMATION | VARIABLE SELECTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Kurdyka-Lojasiewicz (KL) property | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | SUBANALYTIC FUNCTIONS | MINIMIZATION | CONVERGENCE | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | Computer vision | Learning algorithms | Tensors | Algorithms | Image processing | Mathematical analysis | Machine learning | Critical point | Video data | Objective function

Tensile stress | Computational modeling | nuclear norm | Minimization | Linear programming | Data models | proximal linearized minimization (PLM) | Numerical models | nonconvex optimization | Matrix decomposition | Kurdyka–Łojasiewicz (KL) property | tensor completion | Kurdyka-Łojasiewicz (KL) property | FACTORIZATION | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMAGE-RESTORATION | APPROXIMATION | VARIABLE SELECTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Kurdyka-Lojasiewicz (KL) property | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | SUBANALYTIC FUNCTIONS | MINIMIZATION | CONVERGENCE | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | Computer vision | Learning algorithms | Tensors | Algorithms | Image processing | Mathematical analysis | Machine learning | Critical point | Video data | Objective function

Journal Article

10.
Full Text
A Globally Convergent Algorithm for a Constrained Non-Lipschitz Image Restoration Model

JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 03/2020, Volume 83, Issue 1

In this paper, we study a non-Lipschitz and box-constrained model for both piecewise constant and natural image restoration with Gaussian noise removal. It...

MATHEMATICS, APPLIED | Support shrinking | Kurdyka-ojasiewicz property | ALTERNATING MINIMIZATION | High order regularization | Box-constrained | Image restoration | SIGNAL RECONSTRUCTION | Non-Lipschitz optimization | SPACE | RECOVERY | Lower bound theory | NONCONVEX | REGULARIZATION | TOTAL VARIATION MINIMIZATION

MATHEMATICS, APPLIED | Support shrinking | Kurdyka-ojasiewicz property | ALTERNATING MINIMIZATION | High order regularization | Box-constrained | Image restoration | SIGNAL RECONSTRUCTION | Non-Lipschitz optimization | SPACE | RECOVERY | Lower bound theory | NONCONVEX | REGULARIZATION | TOTAL VARIATION MINIMIZATION

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 5/2019, Volume 73, Issue 1, pp. 129 - 158

.... Furthermore, the generated sequence is globally convergent to a stationary point if the objective function satisfies the Kurdyka–Łojasiewicz property...

Nonsmooth | Global convergence | Kurdyka–Łojasiewicz property | Operations Research/Decision Theory | Convex and Discrete Geometry | Inertial proximal gradient method | Mathematics | Operations Research, Management Science | Statistics, general | Nonconvex | Optimization | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | Methods | Business schools | Nonlinear programming | Quadratic programming | Convergence

Nonsmooth | Global convergence | Kurdyka–Łojasiewicz property | Operations Research/Decision Theory | Convex and Discrete Geometry | Inertial proximal gradient method | Mathematics | Operations Research, Management Science | Statistics, general | Nonconvex | Optimization | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | Methods | Business schools | Nonlinear programming | Quadratic programming | Convergence

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 16

...–Łojasiewicz property, the strong convergence of the algorithm is established. Finally, some preliminary numerical results are reported to support the efficiency...

Alternating direction method of multipliers | Kurdyka–Łojasiewicz property | Nonconvex optimization problems | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Convergence | MATHEMATICS | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | ITERATIVE ALGORITHMS | Algorithms | Multipliers | Lagrangian function | Optimization

Alternating direction method of multipliers | Kurdyka–Łojasiewicz property | Nonconvex optimization problems | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Convergence | MATHEMATICS | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | ITERATIVE ALGORITHMS | Algorithms | Multipliers | Lagrangian function | Optimization

Journal Article

Optimization Letters, ISSN 1862-4472, 06/2018, Volume 13, Issue 4, pp. 1 - 20

...)] for solving the minimization of DC functions (difference of two convex functions). Under some suitable assumptions such as level boundedness, Kurdyka-ojasiewicz property...

The second APG algorithm | Nonconvex optimization | Kurdyka–Łojasiewicz property | DC function | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Methods | Algorithms

The second APG algorithm | Nonconvex optimization | Kurdyka–Łojasiewicz property | DC function | MATHEMATICS, APPLIED | Kurdyka-ojasiewicz property | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Methods | Algorithms

Journal Article

International journal of computer mathematics, ISSN 1029-0265, 2016, Volume 94, Issue 8, pp. 1653 - 1669

The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large-scale separable optimization...

Alternating direction method of multipliers | Kurdyka-Łojasiewicz inequality | linear constraints | nonconvex optimization | global convergence | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | MULTIPLIERS | 90C26 | DESCENT METHODS | ALGORITHMS | MINIMIZATION | 49J52 | Kurdyka-ojasiewicz inequality | 65K10 | 49M27 | Linear programming | Critical point | Algorithms | Linear equations | Convergence

Alternating direction method of multipliers | Kurdyka-Łojasiewicz inequality | linear constraints | nonconvex optimization | global convergence | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | MULTIPLIERS | 90C26 | DESCENT METHODS | ALGORITHMS | MINIMIZATION | 49J52 | Kurdyka-ojasiewicz inequality | 65K10 | 49M27 | Linear programming | Critical point | Algorithms | Linear equations | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 2013, Volume 146, Issue 1-2, pp. 459 - 494

.... Building on the powerful Kurdyka–Łojasiewicz property, we derive a self-contained convergence analysis framework and establish that each bounded sequence generated by PALM globally converges to a critical point...

Gauss-Seidel method | Kurdyka–Łojasiewicz property | Theoretical, Mathematical and Computational Physics | Block coordinate descent | Alternating minimization | Mathematics | 90C26 | Nonconvex-nonsmooth minimization | Proximal forward-backward | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 65K10 | 49M27 | 49M37 | Combinatorics | 47J25 | Sparse nonnegative matrix factorization | Kurdyka-Łojasiewicz property | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | Kurdyka-Lojasiewicz property | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | NONNEGATIVE MATRIX FACTORIZATION | Analysis | Management science | Algorithms | Studies | Data smoothing | Mathematical programming | Functions (mathematics) | Construction | Mathematical analysis | Palm | Byproducts | Minimization | Optimization | Optimization and Control

Gauss-Seidel method | Kurdyka–Łojasiewicz property | Theoretical, Mathematical and Computational Physics | Block coordinate descent | Alternating minimization | Mathematics | 90C26 | Nonconvex-nonsmooth minimization | Proximal forward-backward | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 65K10 | 49M27 | 49M37 | Combinatorics | 47J25 | Sparse nonnegative matrix factorization | Kurdyka-Łojasiewicz property | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | Kurdyka-Lojasiewicz property | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | NONNEGATIVE MATRIX FACTORIZATION | Analysis | Management science | Algorithms | Studies | Data smoothing | Mathematical programming | Functions (mathematics) | Construction | Mathematical analysis | Palm | Byproducts | Minimization | Optimization | Optimization and Control

Journal Article

IEEE transactions on signal processing, ISSN 1941-0476, 2018, Volume 66, Issue 20, pp. 5380 - 5391

.... We also provide several guarantees for the convergence and prove that the algorithm globally converges to a critical point of an auxiliary function with the help of the Kurdyka-Łojasiewicz property...

Alternating direction method of multipliers | Nonconvex and nonsmooth minimization | Machine learning algorithms | Kurdyka-Łojasiewicz property | Signal processing algorithms | Minimization | Convex functions | Semi-algebraic functions | Electronic mail | Iteratively reweighted algorithm | Convergence | IMAGE-RESTORATION | MINIMIZATION | APPROXIMATION | ALGORITHMS | Kurdyka-Lojasiewicz property | GLOBAL CONVERGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Critical point | Algorithms | Multipliers | Machine learning

Alternating direction method of multipliers | Nonconvex and nonsmooth minimization | Machine learning algorithms | Kurdyka-Łojasiewicz property | Signal processing algorithms | Minimization | Convex functions | Semi-algebraic functions | Electronic mail | Iteratively reweighted algorithm | Convergence | IMAGE-RESTORATION | MINIMIZATION | APPROXIMATION | ALGORITHMS | Kurdyka-Lojasiewicz property | GLOBAL CONVERGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Critical point | Algorithms | Multipliers | Machine learning

Journal Article

Computational optimization and applications, ISSN 0926-6003, 2017, Volume 67, Issue 3, pp. 489 - 520

.... We derive sufficient conditions on the original problem for the corresponding forward-backward envelope to be a level-bounded and Kurdyka-ojasiewicz function with an exponent...

Kurdyka–Łojasiewicz property | Forward–backward envelope | Difference-of-convex programming | Forward-backward envelope | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | ALGORITHM | CONVERGENCE | DESCENT METHODS | Kurdyka-Lojasiewicz property | Mathematical optimization | Algorithms | Economic models | Computational geometry | Least squares method | Optimization algorithms | Signal processing | Convexity | Continuity (mathematics) | Mathematical programming

Kurdyka–Łojasiewicz property | Forward–backward envelope | Difference-of-convex programming | Forward-backward envelope | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | ALGORITHM | CONVERGENCE | DESCENT METHODS | Kurdyka-Lojasiewicz property | Mathematical optimization | Algorithms | Economic models | Computational geometry | Least squares method | Optimization algorithms | Signal processing | Convexity | Continuity (mathematics) | Mathematical programming

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 07/2017, Volume 67, Issue 3, pp. 443 - 487

.... We propose an algorithmic scheme that enjoys the same global convergence properties of FBS when the problem is convex, or when the objective function possesses the Kurdyka-Aojasiewicz property at its critical points...

Nonsmooth optimization | Quasi-Newton | Line-search methods | Kurdyka–Łojasiewicz | Forward–backward splitting | Kurdyka-Lojasiewicz | MATHEMATICS, APPLIED | SUPERLINEAR CONVERGENCE | PROXIMAL ALGORITHM | INEQUALITY | SUM | DESCENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SHRINKAGE | BFGS METHOD | Forward-backward splitting | NONCONVEX | GLOBAL CONVERGENCE | Electrical engineering | Algorithms | Analysis | Epoxy resins | Methods | Composite functions | Newton methods | Optimization algorithms | Solvers | Nonlinear programming | Optimization | Convergence | Mathematics - Optimization and Control

Nonsmooth optimization | Quasi-Newton | Line-search methods | Kurdyka–Łojasiewicz | Forward–backward splitting | Kurdyka-Lojasiewicz | MATHEMATICS, APPLIED | SUPERLINEAR CONVERGENCE | PROXIMAL ALGORITHM | INEQUALITY | SUM | DESCENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SHRINKAGE | BFGS METHOD | Forward-backward splitting | NONCONVEX | GLOBAL CONVERGENCE | Electrical engineering | Algorithms | Analysis | Epoxy resins | Methods | Composite functions | Newton methods | Optimization algorithms | Solvers | Nonlinear programming | Optimization | Convergence | Mathematics - Optimization and Control

Journal Article

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

.... Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-ojasiewicz inequality...

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