2017, 1, ISBN 9781498763622, Volume 1, xiv, 347 pages

.... Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence...

Iterative methods (Mathematics) | Numerical analysis | Applied Mathematics | Differential Equations | Computational Numerical Analysis

Iterative methods (Mathematics) | Numerical analysis | Applied Mathematics | Differential Equations | Computational Numerical Analysis

Book

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

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

Mathematical programming, ISSN 1436-4646, 2015, Volume 156, Issue 1-2, pp. 433 - 484

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum...

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | MATHEMATICS, APPLIED | ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | CONSTRAINTS | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Computer programming | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | MATHEMATICS, APPLIED | ALGORITHM | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | CONSTRAINTS | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Computer programming | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2015, Volume 61, Issue 4, pp. 1985 - 2007

.... In a nutshell, this algorithm starts with a careful initialization obtained by means of a spectral method, and then refines this initial estimate by iteratively applying novel update rules...

non-convex optimization | Fourier transforms | Accuracy | Diffraction | Computational modeling | Wirtinger derivatives | convergence to global optimum | phase retrieval | Vectors | Optimization | Convergence | Non-convex optimization | X-RAY CRYSTALLOGRAPHY | RECONSTRUCTION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MATRIX COMPLETION | MULTIDIMENSIONAL SEQUENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MAGNITUDE | FOURIER-TRANSFORM | ALLOW | Measurement | Usage | Frequency modulation | Innovations | Signal processing | Convex functions | Mathematical optimization | Iterative methods (Mathematics)

non-convex optimization | Fourier transforms | Accuracy | Diffraction | Computational modeling | Wirtinger derivatives | convergence to global optimum | phase retrieval | Vectors | Optimization | Convergence | Non-convex optimization | X-RAY CRYSTALLOGRAPHY | RECONSTRUCTION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MATRIX COMPLETION | MULTIDIMENSIONAL SEQUENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MAGNITUDE | FOURIER-TRANSFORM | ALLOW | Measurement | Usage | Frequency modulation | Innovations | Signal processing | Convex functions | Mathematical optimization | Iterative methods (Mathematics)

Journal Article

2013, 1st ed., Numerical Mathematics and Scientific Computation, ISBN 9780199655410, Volume 9780199655410, xv, 391

This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations...

Applied Mathematics | Algebra | Sparse matrices | Mathematical optimization | Conjugate gradient method | Cost of computations | Problem of moments | Krylov subspace methods | GMRES | Orthogonal polynomials | Projection methods | Jacobi matrices | Cyclic invariant subspaces | Short recurrences | Continued fractions | Convergence analysis | Iterative methods (Mathematics)

Applied Mathematics | Algebra | Sparse matrices | Mathematical optimization | Conjugate gradient method | Cost of computations | Problem of moments | Krylov subspace methods | GMRES | Orthogonal polynomials | Projection methods | Jacobi matrices | Cyclic invariant subspaces | Short recurrences | Continued fractions | Convergence analysis | Iterative methods (Mathematics)

Book

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2011, Volume 2011, Issue 1, pp. 1 - 18

.... We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process...

monotone mapping | Mathematical and Computational Biology | Mathematics | variational inequality | Topology | demiclosedness principle | strong convergence | asymptotically strict pseudocontractive mapping in the intermediate sense | modified Mann iteration process | fixed point | Analysis | extragradient-like approximation method | Mathematics, general | Applications of Mathematics | Differential Geometry | Asymptotically strict pseudocontractive mapping in the intermediate sense | Strong convergence | Extragradient-like approximation method | Monotone mapping | Variational inequality | Modified mann iteration process | Demiclosedness principle | Fixed point | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | ITERATIVE CONSTRUCTION | WEAK | MATHEMATICS | BANACH-SPACES | INTERMEDIATE SENSE | PSEUDO-CONTRACTIONS | STRICT PSEUDOCONTRACTIVE MAPPINGS | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | OPERATORS | Usage | Inequalities (Mathematics) | Fixed point theory | Convergence (Mathematics) | Point mappings (Mathematics) | Iterative methods (Mathematics) | Tests, problems and exercises | Theorems | Fixed points (mathematics) | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Iterative algorithms | Mapping | Convergence

monotone mapping | Mathematical and Computational Biology | Mathematics | variational inequality | Topology | demiclosedness principle | strong convergence | asymptotically strict pseudocontractive mapping in the intermediate sense | modified Mann iteration process | fixed point | Analysis | extragradient-like approximation method | Mathematics, general | Applications of Mathematics | Differential Geometry | Asymptotically strict pseudocontractive mapping in the intermediate sense | Strong convergence | Extragradient-like approximation method | Monotone mapping | Variational inequality | Modified mann iteration process | Demiclosedness principle | Fixed point | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | ITERATIVE CONSTRUCTION | WEAK | MATHEMATICS | BANACH-SPACES | INTERMEDIATE SENSE | PSEUDO-CONTRACTIONS | STRICT PSEUDOCONTRACTIVE MAPPINGS | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | OPERATORS | Usage | Inequalities (Mathematics) | Fixed point theory | Convergence (Mathematics) | Point mappings (Mathematics) | Iterative methods (Mathematics) | Tests, problems and exercises | Theorems | Fixed points (mathematics) | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Iterative algorithms | Mapping | Convergence

Journal Article

Advances in computational mathematics, ISSN 1019-7168, 2017, Volume 43, Issue 1, pp. 45 - 76

.... We introduce an improved method for transmission at the internal boundaries using perfectly matched layers...

Multigrid method | Computational Mathematics | High-frequency waves | Helmholtz equation | Perfectly matched layers | Applied Mathematics | Domain decomposition | Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Mathematics | Computational Science and Engineering | Mathematical Modeling and Industrial Mathematics | 65N55 | 65N22 | MATHEMATICS, APPLIED | 2D | SOLVER | Analysis | Iterative methods (Mathematics) | Decomposition (Mathematics) | Mathematics - Numerical Analysis

Multigrid method | Computational Mathematics | High-frequency waves | Helmholtz equation | Perfectly matched layers | Applied Mathematics | Domain decomposition | Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Mathematics | Computational Science and Engineering | Mathematical Modeling and Industrial Mathematics | 65N55 | 65N22 | MATHEMATICS, APPLIED | 2D | SOLVER | Analysis | Iterative methods (Mathematics) | Decomposition (Mathematics) | Mathematics - Numerical Analysis

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2013, Volume 2013, Issue 1, pp. 201 - 12

Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e.g...

split feasibility problem | minimum-norm | Mathematical and Computational Biology | Analysis | self-adaptive method | minimization problem | Mathematics, general | Mathematics | Applications of Mathematics | Topology | projection | Differential Geometry | Minimum-norm | Self-adaptive method | Projection | Split feasibility problem | Minimization problem | MATHEMATICS, APPLIED | POLYAK PROJECTION METHOD | VARIATIONAL INEQUALITY PROBLEMS | ITERATIVE ALGORITHMS | MATHEMATICS | SETS | CONVEX MINIMIZATION | OPERATORS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Adaptive control

split feasibility problem | minimum-norm | Mathematical and Computational Biology | Analysis | self-adaptive method | minimization problem | Mathematics, general | Mathematics | Applications of Mathematics | Topology | projection | Differential Geometry | Minimum-norm | Self-adaptive method | Projection | Split feasibility problem | Minimization problem | MATHEMATICS, APPLIED | POLYAK PROJECTION METHOD | VARIATIONAL INEQUALITY PROBLEMS | ITERATIVE ALGORITHMS | MATHEMATICS | SETS | CONVEX MINIMIZATION | OPERATORS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Adaptive control

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

.... By
3 Department of Mathematics and means of the monotone iterative technique and combining with suitable conditions,
Statistics, Curtin University of the existence...

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

Journal Article

2011, Chapman & Hall/CRC numerical analysis and scientific computing, ISBN 9781439869826, xxiii, 303

Book

Mathematical programming, ISSN 1436-4646, 2012, Volume 140, Issue 1, pp. 125 - 161

In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two terms...

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECONVOLUTION | MINIMIZATION | l-Regularization | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECONVOLUTION | MINIMIZATION | l-Regularization | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

Journal Article

Educational studies in mathematics, ISSN 1573-0816, 2018, Volume 100, Issue 3, pp. 231 - 249

There are currently many mathematics anxiety rating scales designed typically for adult and older children populations, yet there remains a lack of assessment tools for younger children (< 7 years of age...

Mathematics anxiety | Mathematics performance | Mathematics Education | Mathematics, general | Factor analysis | Education | Mathematics Anxiety | Test Construction | Factor Analysis | Test Reliability | Young Children | Scores | Test Validity | Anxiety | Predictive Validity | Foreign Countries | Rating Scales

Mathematics anxiety | Mathematics performance | Mathematics Education | Mathematics, general | Factor analysis | Education | Mathematics Anxiety | Test Construction | Factor Analysis | Test Reliability | Young Children | Scores | Test Validity | Anxiety | Predictive Validity | Foreign Countries | Rating Scales

Journal Article

SIAM journal on scientific computing, ISSN 1095-7197, 2012, Volume 34, Issue 3, pp. A1380 - A1405

...; these methods can make great progress initially, but often slow as they approach a solution. In contrast, full-gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration...

data fitting | MATHEMATICS, APPLIED | incremental gradient | optimization | gradient descent | GRADIENT | Fittings | Algorithms | Expenses | Mathematical models | Iterative methods | Sampling | Optimization | Convergence | Other Statistics | Mathematics | Optimization and Control | Statistics | Numerical Analysis | Computer Science

data fitting | MATHEMATICS, APPLIED | incremental gradient | optimization | gradient descent | GRADIENT | Fittings | Algorithms | Expenses | Mathematical models | Iterative methods | Sampling | Optimization | Convergence | Other Statistics | Mathematics | Optimization and Control | Statistics | Numerical Analysis | Computer Science

Journal Article

2016, ISBN 9781498753760, xxix, 309 pages

.... Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors' new method called zeroing dynamics solves time-varying problems...

Neural networks (Computer science) | Newton-Raphson method

Neural networks (Computer science) | Newton-Raphson method

Book