Journal of Water Resources Planning and Management, ISSN 0733-9496, 03/2015, Volume 141, Issue 3, p. 4014060

AbstractVarious multiobjective evolutionary algorithms (MOEAs) have been applied to solve the optimal design problems of a water distribution system (WDS...

Technical Papers | Two-objective design | Water distribution system | Best-known pareto front | Multiobjective evolutionary algorithm | Hybrid algorithm | Benchmark problem | Water distribution systems | WATER RESOURCES | RELIABILITY | ENGINEERING, CIVIL | Algorithms | Benchmark | Best-known Pareto front | EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION | Rehabilitation | EFFICIENT | Water | Usage | Evolutionary algorithms | Analysis | Distribution

Technical Papers | Two-objective design | Water distribution system | Best-known pareto front | Multiobjective evolutionary algorithm | Hybrid algorithm | Benchmark problem | Water distribution systems | WATER RESOURCES | RELIABILITY | ENGINEERING, CIVIL | Algorithms | Benchmark | Best-known Pareto front | EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION | Rehabilitation | EFFICIENT | Water | Usage | Evolutionary algorithms | Analysis | Distribution

Journal Article

Optimization letters, ISSN 1862-4480, 2019, Volume 14, Issue 5, pp. 1193 - 1205

.... The approach is then applied to computing the proximity operator of the sum of weakly convex functions, and particularly to finding the best approximation...

Projector | MATHEMATICS, APPLIED | Linear convergence | Strong convergence | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Resolvent | Douglas-Rachford algorithm | Proximity operator | ALGORITHM | Operator splitting | Best approximation | Peaceman-Rachford algorithm

Projector | MATHEMATICS, APPLIED | Linear convergence | Strong convergence | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Resolvent | Douglas-Rachford algorithm | Proximity operator | ALGORITHM | Operator splitting | Best approximation | Peaceman-Rachford algorithm

Journal Article

Multidimensional Systems and Signal Processing, ISSN 0923-6082, 10/2018, Volume 29, Issue 4, pp. 1739 - 1756

This paper investigates the problem of simultaneous approximation of a prescribed multidimensional frequency response...

Engineering | Multidimensional IIR digital filter | Kolmogorov’s criteria | Sign condition | Signal,Image and Speech Processing | Artificial Intelligence (incl. Robotics) | Chebyshev approximation | Best approximation | Circuits and Systems | Frequency response | H -sets | Electrical Engineering | H-sets | DESIGN | STABILITY PROPERTIES | CONVEX STABILITY | COMPUTER SCIENCE, THEORY & METHODS | Kolmogorov's criteria | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric filters | Electric properties

Engineering | Multidimensional IIR digital filter | Kolmogorov’s criteria | Sign condition | Signal,Image and Speech Processing | Artificial Intelligence (incl. Robotics) | Chebyshev approximation | Best approximation | Circuits and Systems | Frequency response | H -sets | Electrical Engineering | H-sets | DESIGN | STABILITY PROPERTIES | CONVEX STABILITY | COMPUTER SCIENCE, THEORY & METHODS | Kolmogorov's criteria | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric filters | Electric properties

Journal Article

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, ISSN 0764-583X, 04/2019, Volume 53, Issue 2, pp. 551 - 583

Fully-discrete approximations of the Allen-Cahn equation are considered. In particular, we consider schemes of arbitrary order based on a discontinuous Galerkin (in time...

Allen-Cahn equations | MATHEMATICS, APPLIED | 2ND-ORDER | INTERFACE | HILLIARD EQUATION | A-PRIORI | GALERKIN METHODS | FINITE-ELEMENT APPROXIMATION | PARABOLIC PROBLEMS | best approximation error estimates | STOKES | discontinuous time-stepping schemes

Allen-Cahn equations | MATHEMATICS, APPLIED | 2ND-ORDER | INTERFACE | HILLIARD EQUATION | A-PRIORI | GALERKIN METHODS | FINITE-ELEMENT APPROXIMATION | PARABOLIC PROBLEMS | best approximation error estimates | STOKES | discontinuous time-stepping schemes

Journal Article

Foundations of computational mathematics, ISSN 1615-3383, 2014, Volume 14, Issue 6, pp. 1209 - 1242

.... We give analogous results for the homogeneous pencil eigenvalue problem for cubic tensors, i.e., $$m_1=\cdots =m_d$$ m 1 = ⋯ = m d...

Best rank- $$(r_1 , \ldots , r_d)$$ ( r 1 , … , r d ) approximation | Singular vector tuples | Best rank-one approximation | Economics general | 65K05 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14D21 | 15A69 | 15A18 | Vector bundles | Chern classes | Partially symmetric tensors | Numerical Analysis | 65H10 | Applications of Mathematics | Math Applications in Computer Science | Homogeneous pencil eigenvalue problem for cubic tensors | 65D15 | Computer Science, general | Singular value decomposition | r | approximation | Best rank-(r | MATHEMATICS, APPLIED | MAXIMUM | MATHEMATICS | EIGENVALUES | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | Best rank-(r,...,r(d)) approximation | Approximation theory | Vector spaces | Analysis | Tensors (Mathematics) | Vector space | Approximations | Tensors | Approximation | Mathematical analysis | Uniqueness | Eigenvalues | Texts | Vectors (mathematics) | Pencils

Best rank- $$(r_1 , \ldots , r_d)$$ ( r 1 , … , r d ) approximation | Singular vector tuples | Best rank-one approximation | Economics general | 65K05 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14D21 | 15A69 | 15A18 | Vector bundles | Chern classes | Partially symmetric tensors | Numerical Analysis | 65H10 | Applications of Mathematics | Math Applications in Computer Science | Homogeneous pencil eigenvalue problem for cubic tensors | 65D15 | Computer Science, general | Singular value decomposition | r | approximation | Best rank-(r | MATHEMATICS, APPLIED | MAXIMUM | MATHEMATICS | EIGENVALUES | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | Best rank-(r,...,r(d)) approximation | Approximation theory | Vector spaces | Analysis | Tensors (Mathematics) | Vector space | Approximations | Tensors | Approximation | Mathematical analysis | Uniqueness | Eigenvalues | Texts | Vectors (mathematics) | Pencils

Journal Article

6.
Full Text
Neural networks for computing best rank-one approximations of tensors and its applications

Neurocomputing (Amsterdam), ISSN 0925-2312, 2017, Volume 267, pp. 114 - 133

This paper presents the neural dynamical network to compute a best rank-one approximation of a real-valued tensor...

Best rank-one approximation | The local minimal generalized eigenpair | Restricted singular value | Neural network | Rank-one tensor | Restricted singular vector | Symmetric-definite tensor pair | H-eigenpair | The local maximal generalized eigenpair | Generalized tensor eigenpair | Ordinary differential equations | Z-eigenpair | Lyapunov stability theory | Local optimal rank-one approximation | Lyapunov function | SINGULAR-VALUE DECOMPOSITION | SHIFTED POWER METHOD | OPTIMIZATION PROBLEMS | SYMMETRIC TENSORS | INDEPENDENT COMPONENT ANALYSIS | NONNEGATIVE TENSORS | ORDER SUPERSYMMETRIC TENSORS | EIGENPAIRS | PERTURBATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SMALLEST GENERALIZED EIGENVALUE | Rankings | Numerical analysis | Research institutes | Neural networks | Differential equations

Best rank-one approximation | The local minimal generalized eigenpair | Restricted singular value | Neural network | Rank-one tensor | Restricted singular vector | Symmetric-definite tensor pair | H-eigenpair | The local maximal generalized eigenpair | Generalized tensor eigenpair | Ordinary differential equations | Z-eigenpair | Lyapunov stability theory | Local optimal rank-one approximation | Lyapunov function | SINGULAR-VALUE DECOMPOSITION | SHIFTED POWER METHOD | OPTIMIZATION PROBLEMS | SYMMETRIC TENSORS | INDEPENDENT COMPONENT ANALYSIS | NONNEGATIVE TENSORS | ORDER SUPERSYMMETRIC TENSORS | EIGENPAIRS | PERTURBATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SMALLEST GENERALIZED EIGENVALUE | Rankings | Numerical analysis | Research institutes | Neural networks | Differential equations

Journal Article

Journal of combinatorial optimization, ISSN 1573-2886, 2018, Volume 37, Issue 3, pp. 889 - 900

.... An optimization problem, which we term FCSA, is to find an optimum way how clients are assigned to servers such that the largest latency on an interactivity path between two clients...

Best possible approximation | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Bottleneck minimization problem | Combinatorics | Approximation algorithm | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHMS | Algorithms

Best possible approximation | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Bottleneck minimization problem | Combinatorics | Approximation algorithm | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHMS | Algorithms

Journal Article

8.
Full Text
A ‘best points’ interpolation method for efficient approximation of parametrized functions

International journal for numerical methods in engineering, ISSN 1097-0207, 2008, Volume 73, Issue 4, pp. 521 - 543

We present an interpolation method for efficient approximation of parametrized functions...

coefficient‐function approximation | parametrized functions | interpolation points | best points interpolation method | best approximation | Parametrized functions | Best approximation | Best points interpolation method | Coefficient-function approximation | Interpolation points | INTERVAL | POLYNOMIAL INTERPOLATION | TRIANGLE | STATE | SENSOR PLACEMENT | coefficient-function approximation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TETRAHEDRON | REAL FUNCTIONS | SYSTEMS

coefficient‐function approximation | parametrized functions | interpolation points | best points interpolation method | best approximation | Parametrized functions | Best approximation | Best points interpolation method | Coefficient-function approximation | Interpolation points | INTERVAL | POLYNOMIAL INTERPOLATION | TRIANGLE | STATE | SENSOR PLACEMENT | coefficient-function approximation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TETRAHEDRON | REAL FUNCTIONS | SYSTEMS

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 12/2018, Volume 71, Issue 3, pp. 767 - 794

We propose a new modified primal–dual proximal best approximation method for solving convex not necessarily differentiable optimization problems...

Proximal algorithm with memory | Inclusions with maximally monotone operators | Best approximation of the Kuhn–Tucker set | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Attraction property | Optimization | Primal–dual algorithm | Image reconstruction | MATHEMATICS, APPLIED | Primal-dual algorithm | MAXIMAL MONOTONE-OPERATORS | INCLUSIONS | SUM | CONVEX-OPTIMIZATION | COMPOSITE | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Best approximation of the Kuhn-Tucker set | PROJECTIVE SPLITTING METHODS | POINT ALGORITHM | FIXED-POINTS | STRONG-CONVERGENCE | Projectors | Information science | Algorithms | Memory | Computer memory | Approximation | Mathematical analysis | Intersections

Proximal algorithm with memory | Inclusions with maximally monotone operators | Best approximation of the Kuhn–Tucker set | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Attraction property | Optimization | Primal–dual algorithm | Image reconstruction | MATHEMATICS, APPLIED | Primal-dual algorithm | MAXIMAL MONOTONE-OPERATORS | INCLUSIONS | SUM | CONVEX-OPTIMIZATION | COMPOSITE | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Best approximation of the Kuhn-Tucker set | PROJECTIVE SPLITTING METHODS | POINT ALGORITHM | FIXED-POINTS | STRONG-CONVERGENCE | Projectors | Information science | Algorithms | Memory | Computer memory | Approximation | Mathematical analysis | Intersections

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 1/2013, Volume 188, Issue 2, pp. 146 - 166

A number of extremal problems of approximation theory of functions have been solved on the real line $$ \mathbb{R...

entire function of the exponential type | majorant | Fourier transformation | Jackson-type inequality | class of functions | width | Mathematics, general | Best approximation | Mathematics | real axis | modulus of continuity | average ν -width | average ν-width | Toy industry | Analysis

entire function of the exponential type | majorant | Fourier transformation | Jackson-type inequality | class of functions | width | Mathematics, general | Best approximation | Mathematics | real axis | modulus of continuity | average ν -width | average ν-width | Toy industry | Analysis

Journal Article

European journal of operational research, ISSN 0377-2217, 02/2018, Volume 265, Issue 1, pp. 19 - 25

....•Characterizing best approximation from a convex set without convexity of constraints. We study constraint qualifications and necessary and sufficient optimality conditions...

Nonconvex constraints | Best approximation | Necessary and sufficient optimality conditions | Convex programming | Constraint qualifications | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMALITY CONDITIONS | STRONG CHIP | Approximation theory | Mathematical optimization | Analysis

Nonconvex constraints | Best approximation | Necessary and sufficient optimality conditions | Convex programming | Constraint qualifications | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMALITY CONDITIONS | STRONG CHIP | Approximation theory | Mathematical optimization | Analysis

Journal Article

Pure and Applied Geophysics, ISSN 0033-4553, 1/2019, Volume 176, Issue 1, pp. 335 - 344

.... These methods are based on solving the problems of the best approximation of the signal under analysis to signals of a specified class and used in estimating the lag time of one fragment of signal...

Signal waveform | Lag time | Estimate of signal parameters/best approximation problem | Earth Sciences | Geophysics/Geodesy | GEOCHEMISTRY & GEOPHYSICS | best approximation problem | Estimate of signal parameters | Analysis | Atmospheric physics | Amplitude | Random noise | Sound waves | Transformation | Additives | Amplitudes | Approximation | Methodology | Noise | Estimation | Waveforms | Sound propagation | Wave propagation | Detection | Signal detection

Signal waveform | Lag time | Estimate of signal parameters/best approximation problem | Earth Sciences | Geophysics/Geodesy | GEOCHEMISTRY & GEOPHYSICS | best approximation problem | Estimate of signal parameters | Analysis | Atmospheric physics | Amplitude | Random noise | Sound waves | Transformation | Additives | Amplitudes | Approximation | Methodology | Noise | Estimation | Waveforms | Sound propagation | Wave propagation | Detection | Signal detection

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 5/2011, Volume 50, Issue 1, pp. 77 - 91

The best approximation problem to a nonempty closed set in a locally uniformly convex Banach space is considered...

Cone supported sets | 46B20 | Porous sets | Optimization | Economics / Management Science | Metric projection | Baire category | Operations Research/Decision Theory | 41A65 | Best approximation | Computer Science, general | Real Functions | Well-posedness | ROTUNDITY | MATHEMATICS, APPLIED | PERTURBED OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | BANACH-SPACES | Studies | Banach spaces | Approximations | Numerical Analysis | Mathematics

Cone supported sets | 46B20 | Porous sets | Optimization | Economics / Management Science | Metric projection | Baire category | Operations Research/Decision Theory | 41A65 | Best approximation | Computer Science, general | Real Functions | Well-posedness | ROTUNDITY | MATHEMATICS, APPLIED | PERTURBED OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | BANACH-SPACES | Studies | Banach spaces | Approximations | Numerical Analysis | Mathematics

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 07/2019, Volume 19, Issue 3, pp. 483 - 502

We consider DPG methods with optimal test functions and broken test spaces based on ultra-weak formulations of general second-order elliptic problems...

65N12 | Ultra-Weak Formulation | Postprocessing | Duality Arguments | Best Approximation | Superconvergence | DPG Method | 65N30 | MATHEMATICS, APPLIED | CONVERGENCE | Formulations | Norms | Polynomials | Approximation | Test procedures | Convection

65N12 | Ultra-Weak Formulation | Postprocessing | Duality Arguments | Best Approximation | Superconvergence | DPG Method | 65N30 | MATHEMATICS, APPLIED | CONVERGENCE | Formulations | Norms | Polynomials | Approximation | Test procedures | Convection

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 4, pp. 2591 - 2619

We consider the best approximation problem (BAP) of projecting a point onto the intersection of a number of convex sets...

Best approximation problem | Dykstra's algorithm | Alternating minimization | ACCELERATION | MATHEMATICS, APPLIED | MINIMIZATION | CONVEX | alternating minimization | ALGORITHM | DECOMPOSITION | CONVERGENCE | best approximation problem | LEAST-SQUARES

Best approximation problem | Dykstra's algorithm | Alternating minimization | ACCELERATION | MATHEMATICS, APPLIED | MINIMIZATION | CONVEX | alternating minimization | ALGORITHM | DECOMPOSITION | CONVERGENCE | best approximation problem | LEAST-SQUARES

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 12/2013, Volume 7, Issue 6, pp. 1787 - 1805

... with Meromorphic Approximation Alberto A. Condori Received: 18 April 2011 / Accepted: 8 June 2012 / Published online: 18 July 2012 © Springer Basel AG 2012 Abstract Let null...

Nehari–Takagi problem | Operator Theory | Analysis | Superoptimal approximation | Secondary 47B35 | Mathematics, general | Best approximation | 46E40 | Mathematics | Hankel and Toeplitz operators | Badly approximable matrix-valued functions | Primary 47A57 | Nehari-Takagi problem | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS

Nehari–Takagi problem | Operator Theory | Analysis | Superoptimal approximation | Secondary 47B35 | Mathematics, general | Best approximation | 46E40 | Mathematics | Hankel and Toeplitz operators | Badly approximable matrix-valued functions | Primary 47A57 | Nehari-Takagi problem | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2015, Volume 432, Issue 2, pp. 1095 - 1105

...≤∞. Finally, some applications of the results to the best dominated approximation problems are presented...

Strict monotonicity | Uniform monotonicity | Orlicz space | Lower (upper) local uniform monotonicity | Dominated best approximation problems | p-Amemiya norm | P-Amemiya norm | ROTUNDITY | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-LATTICES | Computer science

Strict monotonicity | Uniform monotonicity | Orlicz space | Lower (upper) local uniform monotonicity | Dominated best approximation problems | p-Amemiya norm | P-Amemiya norm | ROTUNDITY | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-LATTICES | Computer science

Journal Article

Journal of non-Newtonian fluid mechanics, ISSN 0377-0257, 2017, Volume 249, pp. 8 - 25

.... For these reasons, a lot of researchers have considered this function to provide its optimal approximation...

Mathematica computer software | Best approximation | Taylor expansion | FENE Model | Inverse Langevin function | Padé approximation | MECHANICS | BRILLOUIN | MODELS | DEFORMATIONS | Fade approximation | STRESS

Mathematica computer software | Best approximation | Taylor expansion | FENE Model | Inverse Langevin function | Padé approximation | MECHANICS | BRILLOUIN | MODELS | DEFORMATIONS | Fade approximation | STRESS

Journal Article