ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 12/2019, Volume 45, Issue 4, pp. 23 - 23

.... Here, we propose a line search algorithm for finding a step size satisfying the strong Wolfe conditions in the vector optimization setting...

Line search algorithm | vector optimization | Wolfe conditions | MATHEMATICS, APPLIED | PROXIMAL METHOD | MULTIOBJECTIVE OPTIMIZATION | NEWTON-LIKE METHODS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMIZATION | PROJECTED GRADIENT-METHOD | CONVERGENCE | STEEPEST DESCENT METHODS | VARIANCE | EFFICIENT SOLUTIONS

Line search algorithm | vector optimization | Wolfe conditions | MATHEMATICS, APPLIED | PROXIMAL METHOD | MULTIOBJECTIVE OPTIMIZATION | NEWTON-LIKE METHODS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMIZATION | PROJECTED GRADIENT-METHOD | CONVERGENCE | STEEPEST DESCENT METHODS | VARIANCE | EFFICIENT SOLUTIONS

Journal Article

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Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Magnetic Resonance Imaging, ISSN 0730-725X, 2011, Volume 29, Issue 9, pp. 1288 - 1303

.... To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept...

Radiology | Constrained independent component analysis | fMRI | Newton-like gradient | Independent component analysis | Augmented Lagrangian | Fixed-point iteration | General linear model | FMRI | NETWORK | TASK | SPATIAL ICA | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Multivariate Analysis | Area Under Curve | Humans | Magnetic Resonance Imaging - methods | Brain Mapping - methods | Models, Statistical | Normal Distribution | Regression Analysis | Algorithms | Brain - pathology | Signal Processing, Computer-Assisted | ROC Curve | Software | Principal Component Analysis | Magnetic resonance imaging | constrained independent component analysis | independent component analysis | augmented Lagrangian, fixed-point iteration | general linear model

Radiology | Constrained independent component analysis | fMRI | Newton-like gradient | Independent component analysis | Augmented Lagrangian | Fixed-point iteration | General linear model | FMRI | NETWORK | TASK | SPATIAL ICA | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Multivariate Analysis | Area Under Curve | Humans | Magnetic Resonance Imaging - methods | Brain Mapping - methods | Models, Statistical | Normal Distribution | Regression Analysis | Algorithms | Brain - pathology | Signal Processing, Computer-Assisted | ROC Curve | Software | Principal Component Analysis | Magnetic resonance imaging | constrained independent component analysis | independent component analysis | augmented Lagrangian, fixed-point iteration | general linear model

Journal Article

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Implicit FEM‐FCT algorithms and discrete Newton methods for transient convection problems

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 06/2008, Volume 57, Issue 6, pp. 761 - 792

...REFERENCES 1 Boris JP , Book DL . Flux‐corrected transport. I. SHASTA, a fluid transport algorithm that works . Journal of Computational Physics 1973 ; 11 : 38...

implicit time stepping | sparse Jacobian evaluation | flux‐corrected transport | Newton‐like solution techniques | finite elements | high‐resolution schemes | Flux-corrected transport | Sparse Jacobian evaluation | Finite elements | Implicit time stepping | Newton-like solution techniques | High-resolution schemes | DESIGN | FINITE-ELEMENT SCHEMES | PHYSICS, FLUIDS & PLASMAS | high-resolution schemes | flux-corrected transport | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS

implicit time stepping | sparse Jacobian evaluation | flux‐corrected transport | Newton‐like solution techniques | finite elements | high‐resolution schemes | Flux-corrected transport | Sparse Jacobian evaluation | Finite elements | Implicit time stepping | Newton-like solution techniques | High-resolution schemes | DESIGN | FINITE-ELEMENT SCHEMES | PHYSICS, FLUIDS & PLASMAS | high-resolution schemes | flux-corrected transport | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS

Journal Article

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On the convergence of inexact two-step Newton-like algorithms using recurrent functions

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2012, Volume 38, Issue 1, pp. 41 - 61

Using our new concept of recurrent functions, we approximate a locally unique solution of a nonlinear equation by an inexact two-step Newton-like algorithm in a Banach space setting...

Semilocal convergence | Computational Mathematics and Numerical Analysis | Mathematics | Theory of Computation | Banach space | Majorizing sequence | Nonlinear Chandrasekhar-type integral equation | Inexact two-step Newton-like algorithm | Green’s kernel | Mathematics of Computing | Appl.Mathematics/Computational Methods of Engineering | Radiative transfer | 65H10 | 65G99 | 49M15 | 65J15 | 47H17 | Green's kernel | Analysis | Algorithms | Studies | Banach spaces | Integrals | Mathematical analysis | Nonlinear equations | Error analysis | Approximation | Integral equations | Mathematical models | Convergence

Semilocal convergence | Computational Mathematics and Numerical Analysis | Mathematics | Theory of Computation | Banach space | Majorizing sequence | Nonlinear Chandrasekhar-type integral equation | Inexact two-step Newton-like algorithm | Green’s kernel | Mathematics of Computing | Appl.Mathematics/Computational Methods of Engineering | Radiative transfer | 65H10 | 65G99 | 49M15 | 65J15 | 47H17 | Green's kernel | Analysis | Algorithms | Studies | Banach spaces | Integrals | Mathematical analysis | Nonlinear equations | Error analysis | Approximation | Integral equations | Mathematical models | Convergence

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 06/2020, Volume 85, p. 105216

....•The new piecewise continuous contact tangent matrices of nonlinear equations in Newton-like algorithm are explicitly derived...

Newton-like algorithm | Contact and wear | Pressure-dependent friction | Bipotential method | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | FATIGUE | PHYSICS, MATHEMATICAL | FRETTING WEAR | UZAWA | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION | MODELS | NUMERICAL-SIMULATION | FINITE-ELEMENT-ANALYSIS | Mechanics | Engineering Sciences

Newton-like algorithm | Contact and wear | Pressure-dependent friction | Bipotential method | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | FATIGUE | PHYSICS, MATHEMATICAL | FRETTING WEAR | UZAWA | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION | MODELS | NUMERICAL-SIMULATION | FINITE-ELEMENT-ANALYSIS | Mechanics | Engineering Sciences

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2011, Volume 49, Issue 2, pp. 574 - 598

.... Time discretization of these dynamics gives algorithms providing new insight into Newton's method for solving monotone inclusions.

Nonautonomous differential equations | Weak asymptotic convergence | Lyapunov analysis | Maximal monotone operators | Newton-like algorithms | Absolutely continuous trajectories | Levenberg-Marquardt algorithms | Dissipative dynamical systems | Numerical convex optimization | dissipative dynamical systems | weak asymptotic convergence | SYSTEM | MATHEMATICS, APPLIED | absolutely continuous trajectories | APPROXIMATIONS | EQUATIONS | nonautonomous differential equations | PROXIMAL POINT ALGORITHM | maximal monotone operators | VARIATIONAL-INEQUALITIES | CONVERGENCE | HILBERT-SPACE | CONVEX MINIMIZATION | OPERATORS | numerical convex optimization | AUTOMATION & CONTROL SYSTEMS | RIEMANNIAN-MANIFOLDS | Studies | Dynamic programming | Asymptotic methods | Convex analysis | Mathematics | Optimization and Control

Nonautonomous differential equations | Weak asymptotic convergence | Lyapunov analysis | Maximal monotone operators | Newton-like algorithms | Absolutely continuous trajectories | Levenberg-Marquardt algorithms | Dissipative dynamical systems | Numerical convex optimization | dissipative dynamical systems | weak asymptotic convergence | SYSTEM | MATHEMATICS, APPLIED | absolutely continuous trajectories | APPROXIMATIONS | EQUATIONS | nonautonomous differential equations | PROXIMAL POINT ALGORITHM | maximal monotone operators | VARIATIONAL-INEQUALITIES | CONVERGENCE | HILBERT-SPACE | CONVEX MINIMIZATION | OPERATORS | numerical convex optimization | AUTOMATION & CONTROL SYSTEMS | RIEMANNIAN-MANIFOLDS | Studies | Dynamic programming | Asymptotic methods | Convex analysis | Mathematics | Optimization and Control

Journal Article

Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering, ISSN 0258-8013, 05/2014, Volume 34, Issue 13, pp. 2196 - 2200

The convergence theorem of Newton-like power flow algorithm was presented based on initial value sensitivity problems of Newton-like power flow algorithm...

The initial value | Initial value sensitivity | Newton-like power flow algorithm | Power flow convergence | Availability | Electrical engineering | Theorems | Algorithms | Computer simulation | Power flow | Mathematical analysis | Convergence

The initial value | Initial value sensitivity | Newton-like power flow algorithm | Power flow convergence | Availability | Electrical engineering | Theorems | Algorithms | Computer simulation | Power flow | Mathematical analysis | Convergence

Journal Article

Statistical Papers, ISSN 0932-5026, 11/2014, Volume 55, Issue 4, pp. 983 - 1000

.... An efficient Newton-like optimization algorithm on manifolds is developed to obtain the maximum likelihood estimates of the parameters...

Newton-like algorithm | Manifold | Multimodal distribution | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Economic Theory | Fourier series | 62H11 | Statistics | 62H12 | HYPERSPHERE | MODELS | STATISTICS & PROBABILITY | PROBABILITY DENSITY | Mathematical optimization | Analysis | Algorithms | Studies | Optimization algorithms | Fourier analysis | Mathematics | Mathematical models | Statistical methods | Volcanoes | Trigonometry | Data sets | Samples | Three dimensional | Sums

Newton-like algorithm | Manifold | Multimodal distribution | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Economic Theory | Fourier series | 62H11 | Statistics | 62H12 | HYPERSPHERE | MODELS | STATISTICS & PROBABILITY | PROBABILITY DENSITY | Mathematical optimization | Analysis | Algorithms | Studies | Optimization algorithms | Fourier analysis | Mathematics | Mathematical models | Statistical methods | Volcanoes | Trigonometry | Data sets | Samples | Three dimensional | Sums

Journal Article

Applied numerical mathematics, ISSN 0168-9274, 2018, Volume 132, pp. 22 - 34

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of...

Inexact Newton-like method | Constrained nonlinear systems | Conditional gradient method | Local convergence | INJECTIVE-OVERDETERMINED SYSTEMS | MATHEMATICS, APPLIED | MAJORANT CONDITION | ALGORITHM | EQUATIONS | CONVERGENCE BEHAVIOR | SIMPLE BOUNDS | OPTIMIZATION

Inexact Newton-like method | Constrained nonlinear systems | Conditional gradient method | Local convergence | INJECTIVE-OVERDETERMINED SYSTEMS | MATHEMATICS, APPLIED | MAJORANT CONDITION | ALGORITHM | EQUATIONS | CONVERGENCE BEHAVIOR | SIMPLE BOUNDS | OPTIMIZATION

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 09/2009, Volume 57, Issue 9, pp. 3498 - 3511

... estimates of the gradient and Hessian based on an incomplete Cholesky decomposition. In contrast to other efficient kernel-based ICA algorithms, FastKICA is applicable to any twice differentiable kernel function...

Optimization methods | Independent component analysis | Extraterrestrial measurements | Parametric statistics | Hilbert-Schmidt independence criterion | Cybernetics | independent component analysis (ICA) | Machine learning | kernel methods | Particle measurements | Approximate Newton-like methods | Computational efficiency | Kernel | Mutual information | orthogonal group | Kernel methods | Orthogonal group | Independent component analysis (ICA) | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Evaluation | Usage | Kurtosis | Research | Kernel functions | Studies | Models | Algorithms | Kernels | Mathematical models | Criteria | Estimates | Optimization

Optimization methods | Independent component analysis | Extraterrestrial measurements | Parametric statistics | Hilbert-Schmidt independence criterion | Cybernetics | independent component analysis (ICA) | Machine learning | kernel methods | Particle measurements | Approximate Newton-like methods | Computational efficiency | Kernel | Mutual information | orthogonal group | Kernel methods | Orthogonal group | Independent component analysis (ICA) | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Evaluation | Usage | Kurtosis | Research | Kernel functions | Studies | Models | Algorithms | Kernels | Mathematical models | Criteria | Estimates | Optimization

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 11/2014, Volume 35, Issue 11, pp. 1476 - 1499

In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using...

Derivative free method | Semilocal convergence | Divided difference | Steffensen-type method | Banach space | Recurrence relations | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | THEOREM

Derivative free method | Semilocal convergence | Divided difference | Steffensen-type method | Banach space | Recurrence relations | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | THEOREM

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 06/2015, Volume 165, Issue 3, pp. 874 - 900

.... As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailed.

Nonconvex and nonsmooth optimization | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | Gauss-Seidel method | GRADIENT-LIKE SYSTEMS | Convergence rates | PROXIMAL ALGORITHM | Variable metric | THRESHOLDING ALGORITHM | EQUATIONS | SPARSE | Newton-like method | Descent methods | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIUM | OPTIMIZATION | FLOWS | MONOTONE-OPERATORS | Analysis | Methods | Algorithms

Nonconvex and nonsmooth optimization | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | Gauss-Seidel method | GRADIENT-LIKE SYSTEMS | Convergence rates | PROXIMAL ALGORITHM | Variable metric | THRESHOLDING ALGORITHM | EQUATIONS | SPARSE | Newton-like method | Descent methods | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIUM | OPTIMIZATION | FLOWS | MONOTONE-OPERATORS | Analysis | Methods | Algorithms

Journal Article

International journal of computer mathematics, ISSN 0020-7160, 2013, Volume 90, Issue 3, pp. 691 - 704

We introduce a Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting. Then, we present a local convergence analysis for...

Newton's method | recurrence relations | Steffensen-type method | Banach space | divided difference | derivative-free method | Divided difference | Newton’s method | Derivative-free method | Recurrence relations | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | 47H99 | 65G99 | 49M15 | 65J15 | Nonlinear equations | Algorithms | Computer simulation | Chebyshev approximation | Mathematical models | Optimization | Convergence

Newton's method | recurrence relations | Steffensen-type method | Banach space | divided difference | derivative-free method | Divided difference | Newton’s method | Derivative-free method | Recurrence relations | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | 47H99 | 65G99 | 49M15 | 65J15 | Nonlinear equations | Algorithms | Computer simulation | Chebyshev approximation | Mathematical models | Optimization | Convergence

Journal Article

Numerical Algorithms, ISSN 1017-1398, 10/2013, Volume 64, Issue 2, pp. 295 - 309

... by Newton’s method and the doubling algorithm. When the two diagonal blocks of the matrix K have both large and small diagonal entries, the doubling algorithm often requires many more iterations than Newton’s method...

Monotone convergence | Chebyshev’s method | Numeric Computing | Minimal nonnegative solution | Theory of Computation | Newton-like method | Algebraic Riccati equation | Algorithms | Algebra | 15A24 | Numerical Analysis | 65F30 | Computer Science | M -matrix | 65H10 | M-matrix | Chebyshev's method | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | DOUBLING-ALGORITHM | Analysis | Methods | Newton methods | Chebyshev approximation | Mathematical models | Riccati equation | Iterative methods | Convergence

Monotone convergence | Chebyshev’s method | Numeric Computing | Minimal nonnegative solution | Theory of Computation | Newton-like method | Algebraic Riccati equation | Algorithms | Algebra | 15A24 | Numerical Analysis | 65F30 | Computer Science | M -matrix | 65H10 | M-matrix | Chebyshev's method | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | DOUBLING-ALGORITHM | Analysis | Methods | Newton methods | Chebyshev approximation | Mathematical models | Riccati equation | Iterative methods | Convergence

Journal Article

Journal of Harbin Institute of Technology (New Series), ISSN 1005-9113, 12/2007, Volume 14, Issue 6, pp. 803 - 806

Journal Article

Numerical Algorithms, ISSN 1017-1398, 6/2016, Volume 72, Issue 2, pp. 377 - 392

In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by...

Inexact Gauss-Newton like methods | Algorithms | Algebra | Majorant condition | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Local convergence | Injective-overdetermined systems of equations | MATHEMATICS, APPLIED | LOCAL CONVERGENCE ANALYSIS | UNIQUENESS

Inexact Gauss-Newton like methods | Algorithms | Algebra | Majorant condition | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Local convergence | Injective-overdetermined systems of equations | MATHEMATICS, APPLIED | LOCAL CONVERGENCE ANALYSIS | UNIQUENESS

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 04/2013, Volume 33, Issue 2, pp. 481 - 514

We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is a connected part of the...

complete geodesic | positive semidefinite cone | quotient manifold | embedded submanifold | homogeneous space | low-rank matrix | MATHEMATICS, APPLIED | NEWTON-LIKE METHOD | MANIFOLDS | OPTIMIZATION | ALGORITHMS | Approximation | Quotients | Mathematical analysis | Images | Exact solutions | Matrices | Vectors (mathematics) | Matrix methods

complete geodesic | positive semidefinite cone | quotient manifold | embedded submanifold | homogeneous space | low-rank matrix | MATHEMATICS, APPLIED | NEWTON-LIKE METHOD | MANIFOLDS | OPTIMIZATION | ALGORITHMS | Approximation | Quotients | Mathematical analysis | Images | Exact solutions | Matrices | Vectors (mathematics) | Matrix methods

Journal Article

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Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations

INFORMS journal on computing, ISSN 1526-5528, 2019, Volume 31, Issue 2, pp. 235 - 250

In this paper, we propose the continuous variable neighborhood search method for finding all the solutions to a nonlinear system of equations (NSEs). We...

continuous optimization | system of nonlinear equations | variable neighborhood search | direct search methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION ALGORITHM | NEWTON-LIKE METHOD | ITERATIVE METHOD | LESS | Nonlinear theories | Research | Search theory | Mathematical optimization

continuous optimization | system of nonlinear equations | variable neighborhood search | direct search methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION ALGORITHM | NEWTON-LIKE METHOD | ITERATIVE METHOD | LESS | Nonlinear theories | Research | Search theory | Mathematical optimization

Journal Article

SIAM journal on optimization, ISSN 1095-7189, 2002, Volume 13, Issue 3, pp. 805 - 841

We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes nonlinear...

Semismoothness | Optimal control problems | Superlinear convergence | Newton-like methods | Nonlinear complementarity problems | Superposition operators | Generalized differentials | MATHEMATICS, APPLIED | nonlinear complementarity problems | APPROXIMATIONS | STRATEGY | CALCULUS | superposition operators | semismoothness | VARIATIONAL INEQUALITY | ALGORITHMS | optimal control problems | generalized differentials | NONSMOOTH EQUATIONS | CONVERGENCE | MAPPINGS | superlinear convergence | NONLINEAR COMPLEMENTARITY-PROBLEMS | OPTIMIZATION

Semismoothness | Optimal control problems | Superlinear convergence | Newton-like methods | Nonlinear complementarity problems | Superposition operators | Generalized differentials | MATHEMATICS, APPLIED | nonlinear complementarity problems | APPROXIMATIONS | STRATEGY | CALCULUS | superposition operators | semismoothness | VARIATIONAL INEQUALITY | ALGORITHMS | optimal control problems | generalized differentials | NONSMOOTH EQUATIONS | CONVERGENCE | MAPPINGS | superlinear convergence | NONLINEAR COMPLEMENTARITY-PROBLEMS | OPTIMIZATION

Journal Article

Algorithms, ISSN 1999-4893, 2015, Volume 8, Issue 3, pp. 656 - 668

... Algorithms 2015, 8, 656-668; doi:10.3390/a8030656 OPEN ACCESS ISSN 1999-4893 www.mdpi.com/journal/algorithms Juan Liang 1,, Xiaowu Li 2,,*, Zhinan Wu 3...

Nonlinear equation | High-order convergence | Iterative methods | Newton-like method | Multiple roots | Nonlinear equations | Algorithms | Newton methods | Roots | Mathematical models | Convergence | newton-like method | iterative methods | high-order convergence | multiple roots | nonlinear equation

Nonlinear equation | High-order convergence | Iterative methods | Newton-like method | Multiple roots | Nonlinear equations | Algorithms | Newton methods | Roots | Mathematical models | Convergence | newton-like method | iterative methods | high-order convergence | multiple roots | nonlinear equation

Journal Article

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