Mathematical Programming, ISSN 0025-5610, 2/2013, Volume 137, Issue 1, 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...

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 | GRADIENT-LIKE SYSTEMS | EVOLUTION-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SETS | OPTIMIZATION | PROJECTIONS | 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 | GRADIENT-LIKE SYSTEMS | EVOLUTION-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SETS | OPTIMIZATION | PROJECTIONS | POINT ALGORITHM | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2017, Volume 346, pp. 131 - 151

This paper presents a two-dimensional immersed boundary method for fluid–structure interaction with compressible multiphase flows involving large structure...

Fluid–structure interaction | Multiphase flow | Large structure deformations | Immersed-boundary method | Shock wave | Viscous compressible flow | ELASTIC FORCES | NODAL COORDINATE FORMULATION | INCOMPRESSIBLE VISCOUS-FLOW | UNIFORM-FLOW | SIMULATION | PHYSICS, MATHEMATICAL | Fluid-structure interaction | CARTESIAN GRID METHOD | SHOCK-CAPTURING SCHEMES | INTERFACE METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | BIOLOGICAL-SYSTEMS | Fluid dynamics | Analysis | Methods | HYPERSONIC FLOW | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | FLUID-STRUCTURE INTERACTIONS | PLATES | TWO-DIMENSIONAL CALCULATIONS | FINITE ELEMENT METHOD | LAGRANGIAN FUNCTION | SHOCK WAVES | FINITE DIFFERENCE METHOD | FLUID MECHANICS | NAVIER-STOKES EQUATIONS | NONLINEAR PROBLEMS | COMPRESSIBLE FLOW | MULTIPHASE FLOW | EXPERIMENTAL DATA | CYLINDRICAL CONFIGURATION

Fluid–structure interaction | Multiphase flow | Large structure deformations | Immersed-boundary method | Shock wave | Viscous compressible flow | ELASTIC FORCES | NODAL COORDINATE FORMULATION | INCOMPRESSIBLE VISCOUS-FLOW | UNIFORM-FLOW | SIMULATION | PHYSICS, MATHEMATICAL | Fluid-structure interaction | CARTESIAN GRID METHOD | SHOCK-CAPTURING SCHEMES | INTERFACE METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | BIOLOGICAL-SYSTEMS | Fluid dynamics | Analysis | Methods | HYPERSONIC FLOW | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | FLUID-STRUCTURE INTERACTIONS | PLATES | TWO-DIMENSIONAL CALCULATIONS | FINITE ELEMENT METHOD | LAGRANGIAN FUNCTION | SHOCK WAVES | FINITE DIFFERENCE METHOD | FLUID MECHANICS | NAVIER-STOKES EQUATIONS | NONLINEAR PROBLEMS | COMPRESSIBLE FLOW | MULTIPHASE FLOW | EXPERIMENTAL DATA | CYLINDRICAL CONFIGURATION

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 06/2018, Volume 114, Issue 12, pp. 1262 - 1290

Summary In this paper, a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated...

interelement continuity of the tractions | mixed finite element formulation | pointwise equilibrium of forces | stress singularity | curvilinear coordinates | ELASTICITY | DISCRETIZATION | ENERGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | OPERATOR | FORMULATION | Finite element method | Methods | Elasticity | Lagrange multiplier | Lagrange multipliers | Energy conservation | Equilibrium | Mathematics - Numerical Analysis

interelement continuity of the tractions | mixed finite element formulation | pointwise equilibrium of forces | stress singularity | curvilinear coordinates | ELASTICITY | DISCRETIZATION | ENERGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | OPERATOR | FORMULATION | Finite element method | Methods | Elasticity | Lagrange multiplier | Lagrange multipliers | Energy conservation | Equilibrium | Mathematics - Numerical Analysis

Journal Article

1985, 3rd. ed. --, ISBN 0120598205, xxii, 985

Book

1970, 2nd ed., ISBN 9780120598519, xx, 815

Book

1984, Computing. Supplementum, ISBN 9783211818329, Volume 5., ix, 242

Book

Journal of Chemical Physics, ISSN 0021-9606, 05/2013, Volume 138, Issue 18, p. 184102

The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use...

NUDGED ELASTIC BAND | CHEMICAL-REACTIONS | FINDING TRANSITION-STATES | STATIONARY-POINTS | POTENTIAL-ENERGY SURFACES | EQUILIBRIUM GEOMETRIES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | SADDLE-POINTS | CHEMISTRY, PHYSICAL | GEOMETRY OPTIMIZATION | DENSITY-FUNCTIONAL THEORY | REACTION PATHWAYS | Tangents | Interpolation | Mathematical models | Computational efficiency | Strings | Optimization | Convergence | Cartesian coordinates

NUDGED ELASTIC BAND | CHEMICAL-REACTIONS | FINDING TRANSITION-STATES | STATIONARY-POINTS | POTENTIAL-ENERGY SURFACES | EQUILIBRIUM GEOMETRIES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | SADDLE-POINTS | CHEMISTRY, PHYSICAL | GEOMETRY OPTIMIZATION | DENSITY-FUNCTIONAL THEORY | REACTION PATHWAYS | Tangents | Interpolation | Mathematical models | Computational efficiency | Strings | Optimization | Convergence | Cartesian coordinates

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2009, Volume 117, Issue 1, pp. 387 - 423

We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained...

Global convergence | 65K05 | Mathematical and Computational Physics | 90C06 | Error bound | Mathematics | 90C26 | Coordinate descent | Linear convergence rate | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | 90C55 | Nonsmooth optimization | 49M27 | 49M37 | Combinatorics | REGRESSION | MATHEMATICS, APPLIED | error bound | CONTINUOUSLY DIFFERENTIABLE FUNCTION | linear convergence rate | ASCENT METHODS | global convergence | ALGORITHM | coordinate descent | nonsmooth optimization | LINEAR CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONDIFFERENTIABLE OPTIMIZATION PROBLEMS | CONSTRAINTS | UNCONSTRAINED OPTIMIZATION | WAVELET SHRINKAGE | CONVEX MINIMIZATION | Studies | Optimization | Mathematical programming

Global convergence | 65K05 | Mathematical and Computational Physics | 90C06 | Error bound | Mathematics | 90C26 | Coordinate descent | Linear convergence rate | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | 90C55 | Nonsmooth optimization | 49M27 | 49M37 | Combinatorics | REGRESSION | MATHEMATICS, APPLIED | error bound | CONTINUOUSLY DIFFERENTIABLE FUNCTION | linear convergence rate | ASCENT METHODS | global convergence | ALGORITHM | coordinate descent | nonsmooth optimization | LINEAR CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONDIFFERENTIABLE OPTIMIZATION PROBLEMS | CONSTRAINTS | UNCONSTRAINED OPTIMIZATION | WAVELET SHRINKAGE | CONVEX MINIMIZATION | Studies | Optimization | Mathematical programming

Journal Article

JOURNAL OF COMPUTATIONAL MATHEMATICS, ISSN 0254-9409, 2018, Volume 36, Issue 3, pp. 404 - 425

We propose a parallel stochastic Newton method (PSN) for minimizing unconstrained smooth convex functions. We analyze the method in the strongly convex case,...

MATHEMATICS | stochastic algorithms | MATHEMATICS, APPLIED | parallel methods | optimization | COORDINATE DESCENT | Newton's method

MATHEMATICS | stochastic algorithms | MATHEMATICS, APPLIED | parallel methods | optimization | COORDINATE DESCENT | Newton's method

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2016, Volume 304, pp. 452 - 478

The numerical manifold method (NMM) surmounting the mesh dependence has successfully solved very complicated problems involving small deformation and large...

Strain–rotation decomposition | Updated co-moving coordinate | Large deformation analysis | Numerical manifold method | Dynamic formulation | Strain-rotation decomposition | MESHFREE METHOD | LATTICE SPRING MODEL | WEAK DISCONTINUITIES | LARGE-DEFORMATION ANALYSIS | FORMULATION | ARBITRARY EVOLVING CRACKS | KERNEL PARTICLE METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | UNITY METHOD | SOLID MECHANICS | FINITE-ELEMENT-METHOD | Manifolds | Theorems | Dynamic tests | Deformation | Upgrading | Dynamics | Mathematical models | Decomposition

Strain–rotation decomposition | Updated co-moving coordinate | Large deformation analysis | Numerical manifold method | Dynamic formulation | Strain-rotation decomposition | MESHFREE METHOD | LATTICE SPRING MODEL | WEAK DISCONTINUITIES | LARGE-DEFORMATION ANALYSIS | FORMULATION | ARBITRARY EVOLVING CRACKS | KERNEL PARTICLE METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | UNITY METHOD | SOLID MECHANICS | FINITE-ELEMENT-METHOD | Manifolds | Theorems | Dynamic tests | Deformation | Upgrading | Dynamics | Mathematical models | Decomposition

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 07/2019, Volume 78, Issue 2, pp. 318 - 334

We present a new high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas and solid dynamics. The evolution equations for specific volume,...

Discontinuous Galerkin | Hydrodynamics | Solid dynamics | Lagrangian | Compressible flows | Shocks | MATHEMATICS, APPLIED | DISCRETIZATION | EQUATIONS | Fluid dynamics | Analysis | Methods | Specific volume | Mathematical analysis | Dynamic stability | Evolution | Taylor series | Galerkin method | Polynomials | Velocity gradient | Time integration | Internal energy | Cartesian coordinates | MATHEMATICS AND COMPUTING | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | compressible flows | shocks | solid dynamics

Discontinuous Galerkin | Hydrodynamics | Solid dynamics | Lagrangian | Compressible flows | Shocks | MATHEMATICS, APPLIED | DISCRETIZATION | EQUATIONS | Fluid dynamics | Analysis | Methods | Specific volume | Mathematical analysis | Dynamic stability | Evolution | Taylor series | Galerkin method | Polynomials | Velocity gradient | Time integration | Internal energy | Cartesian coordinates | MATHEMATICS AND COMPUTING | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | compressible flows | shocks | solid dynamics

Journal Article

Computational Mechanics, ISSN 0178-7675, 5/2007, Volume 39, Issue 6, pp. 859 - 877

In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle is greater than 180° and the...

Engineering | Mechanics, Fluids, Thermodynamics | Gauss quadrature | Strain smoothing | Finite element method (FEM) | Computational Science and Engineering | Numerical and Computational Methods in Engineering | Theoretical and Applied Mechanics | Smoothed finite element method (SFEM) | Isoparametric element | CONFORMING NODAL INTEGRATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | strain smoothing | MESHLESS METHODS | POINT INTERPOLATION | smoothed finite element method (SFEM) | finite element method (FEM) | isoparametric element | Finite element method | Coordinate transformations | Smoothing | Mathematical analysis | Quadrilaterals | Mapping | Finite element analysis | Nonlinear programming

Engineering | Mechanics, Fluids, Thermodynamics | Gauss quadrature | Strain smoothing | Finite element method (FEM) | Computational Science and Engineering | Numerical and Computational Methods in Engineering | Theoretical and Applied Mechanics | Smoothed finite element method (SFEM) | Isoparametric element | CONFORMING NODAL INTEGRATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | strain smoothing | MESHLESS METHODS | POINT INTERPOLATION | smoothed finite element method (SFEM) | finite element method (FEM) | isoparametric element | Finite element method | Coordinate transformations | Smoothing | Mathematical analysis | Quadrilaterals | Mapping | Finite element analysis | Nonlinear programming

Journal Article

14.
Full Text
Evaluating minimum zone flatness error using new method—Bundle of plains through one point

Precision Engineering, ISSN 0141-6359, 01/2016, Volume 43, pp. 554 - 562

An attempt was made to create a new software solution for evaluating minimum zone (MZ) based flatness error using data acquired from a coordinate measuring...

CMM | Flatness error | One Point Plane Bundle Method | Minimum zone | Analytic geometry | NANOSCIENCE & NANOTECHNOLOGY | STRAIGHTNESS | TOLERANCE EVALUATION | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | ENGINEERING, MANUFACTURING | VERIFICATION | SURFACES | Permissible error | Errors | Coordinate measuring machines | Planes | Least squares method | Transformations | Acceptability | Flatness

CMM | Flatness error | One Point Plane Bundle Method | Minimum zone | Analytic geometry | NANOSCIENCE & NANOTECHNOLOGY | STRAIGHTNESS | TOLERANCE EVALUATION | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | ENGINEERING, MANUFACTURING | VERIFICATION | SURFACES | Permissible error | Errors | Coordinate measuring machines | Planes | Least squares method | Transformations | Acceptability | Flatness

Journal Article

15.
Full Text
A second-order method for strongly convex (Formula presented.) -regularization problems

Mathematical Programming, ISSN 0025-5610, 03/2016, Volume 156, Issue 1-2, pp. 189 - 219

In this paper a robust second-order method is developed for the solution of strongly convex -regularized problems. The main aim is to make the proposed method...

Iteration complexity | Strongly convex optimization | Newton conjugate-gradients method | Second-order methods | (Formula presented.) -Regularization | COORDINATE DESCENT METHOD | REGRESSION | SUPPORT VECTOR MACHINES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SHRINKAGE | LASSO | l-Regularization | Least squares method | Mathematical analysis | Machine learning | Texts | Mathematical models | Iterative methods | Convergence | Mathematical programming

Iteration complexity | Strongly convex optimization | Newton conjugate-gradients method | Second-order methods | (Formula presented.) -Regularization | COORDINATE DESCENT METHOD | REGRESSION | SUPPORT VECTOR MACHINES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SHRINKAGE | LASSO | l-Regularization | Least squares method | Mathematical analysis | Machine learning | Texts | Mathematical models | Iterative methods | Convergence | Mathematical programming

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 2014, Volume 141, Issue 16, p. 164113

The equation-of-motion coupled cluster method employing the complex absorbing potential has been used to investigate the low energy electron scattering by CO2....

COORDINATE METHOD | CROSS-SECTIONS | TEMPORARY ANIONS | EXCITATION-ENERGIES | STABILIZATION METHOD | CCSD METHOD | METASTABLE ANIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | GENERAL FORMALISM | CHEMISTRY, PHYSICAL | ELECTRON PROPAGATOR THEORY | RESONANCE STATES

COORDINATE METHOD | CROSS-SECTIONS | TEMPORARY ANIONS | EXCITATION-ENERGIES | STABILIZATION METHOD | CCSD METHOD | METASTABLE ANIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | GENERAL FORMALISM | CHEMISTRY, PHYSICAL | ELECTRON PROPAGATOR THEORY | RESONANCE STATES

Journal Article

The Chemical Record, ISSN 1527-8999, 10/2016, Volume 16, Issue 5, pp. 2232 - 2248

In this account, a technical overview of the artificial force induced reaction (AFIR) method is presented. The AFIR method is one of the automated...

intrinsic reaction coordinate | conical intersections | transition states | artificial force induced reaction (AFIR) | potential energy surface | NUDGED ELASTIC BAND | TRANSITION-STATE STRUCTURES | CONICAL INTERSECTION STRUCTURES | HYPERSPHERE SEARCH METHOD | REACTION PATHWAYS | CHEMISTRY, MULTIDISCIPLINARY | AUTOMATED DISCOVERY | DETERMINING REACTION PATHS | SYSTEMATIC EXPLORATION | SADDLE-POINTS | DENSITY-FUNCTIONAL THEORY | Methods | Force and energy | Dissociation

intrinsic reaction coordinate | conical intersections | transition states | artificial force induced reaction (AFIR) | potential energy surface | NUDGED ELASTIC BAND | TRANSITION-STATE STRUCTURES | CONICAL INTERSECTION STRUCTURES | HYPERSPHERE SEARCH METHOD | REACTION PATHWAYS | CHEMISTRY, MULTIDISCIPLINARY | AUTOMATED DISCOVERY | DETERMINING REACTION PATHS | SYSTEMATIC EXPLORATION | SADDLE-POINTS | DENSITY-FUNCTIONAL THEORY | Methods | Force and energy | Dissociation

Journal Article