2004, Progress in nonlinear differential equations and their applications, ISBN 0817640843, Volume 58, xii, 304

Book

SIAM journal on scientific computing, ISSN 1095-7197, 2018, Volume 40, Issue 2, pp. A629 - A652

A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB...

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

Journal Article

1977, Mathematics in science & engineering, ISBN 0120893509, Volume 131, xi, 147

Book

European Journal of Operational Research, ISSN 0377-2217, 05/2016, Volume 250, Issue 3, pp. 827 - 841

...–Jacobi–Bellman equations, and can be readily employed in a very general setting, namely continuous or discrete re-balancing, jump-diffusions with finite activity, and realistic portfolio constraints...

Investment analysis | Constrained pre-commitment mean-variance | Finance | HJB equation | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RETURNS | OPTIMIZATION | DIFFUSION | SELECTION | POINTS | JUMP | EFFICIENCY | Decision-making | Hamilton-Jacobi equations | Analysis | Investments

Investment analysis | Constrained pre-commitment mean-variance | Finance | HJB equation | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RETURNS | OPTIMIZATION | DIFFUSION | SELECTION | POINTS | JUMP | EFFICIENCY | Decision-making | Hamilton-Jacobi equations | Analysis | Investments

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 2, pp. 719 - 732

.... This approximation process is also applied to the viscosity solutions of the discounted Hamilton–Jacobi equations.

Aubry–Mather theory | Weak KAM theory | Hamilton–Jacobi equations | Lasry–Lions regularization | MATHEMATICS | Hamilton-Jacobi equations | HILBERT-SPACES | SET | LAX-OLEINIK | LEMMA | POINT-OF-VIEW | DYNAMICS | Lasry-Lions regularization | Aubry-Mather theory | REGULARIZATION

Aubry–Mather theory | Weak KAM theory | Hamilton–Jacobi equations | Lasry–Lions regularization | MATHEMATICS | Hamilton-Jacobi equations | HILBERT-SPACES | SET | LAX-OLEINIK | LEMMA | POINT-OF-VIEW | DYNAMICS | Lasry-Lions regularization | Aubry-Mather theory | REGULARIZATION

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2018, Volume 173, Issue 3-4, pp. 1063 - 1098

...Probab. Theory Relat. Fields (2019) 173:1063–1098 https://doi.org/10.1007/s00440-018-0848-7 Regularization by noise for stochastic Hamilton–Jacobi equations...

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Journal Article

European Journal of Control, ISSN 0947-3580, 09/2017, Volume 37, pp. 70 - 74

This paper presents a computational method to deal with the Hamilton–Jacobi–Bellman equation with respect to a nonlinear optimal control problem...

Hamilton–Jacobi–Bellman equation | Global minimizer flow | Nonlinear minimization | Feedback optimal control | Difference equation | Hamilton-Jacobi-Bellman equation | AUTOMATION & CONTROL SYSTEMS | Hamilton-Jacobi equations | Research | Dynamic programming | Feedback control systems | Methods | Mathematical optimization | Economic models | Nonlinear equations | Control systems | Optimization | Problems | Feedback | Optimal control | Ordinary differential equations | Queuing theory | Control theory | Iterative methods | Nonlinear control

Hamilton–Jacobi–Bellman equation | Global minimizer flow | Nonlinear minimization | Feedback optimal control | Difference equation | Hamilton-Jacobi-Bellman equation | AUTOMATION & CONTROL SYSTEMS | Hamilton-Jacobi equations | Research | Dynamic programming | Feedback control systems | Methods | Mathematical optimization | Economic models | Nonlinear equations | Control systems | Optimization | Problems | Feedback | Optimal control | Ordinary differential equations | Queuing theory | Control theory | Iterative methods | Nonlinear control

Journal Article

ASYMPTOTIC ANALYSIS, ISSN 0921-7134, 2019, Volume 115, Issue 1-2, pp. 63 - 94

.... Solutions of the rescaled equations are known to satisfy a Hamilton-Jacobi equation in the formal limit epsilon -> 0...

renewal equation | MATHEMATICS, APPLIED | WKB approximation | Hamilton-Jacobi equation | Age-structured PDE | CYTOPLASM | DYNAMICS | DIFFUSION | anomalous diffusion | MODEL | AGE | Constraining | Mathematics - Analysis of PDEs

renewal equation | MATHEMATICS, APPLIED | WKB approximation | Hamilton-Jacobi equation | Age-structured PDE | CYTOPLASM | DYNAMICS | DIFFUSION | anomalous diffusion | MODEL | AGE | Constraining | Mathematics - Analysis of PDEs

Journal Article

Journal of process control, ISSN 0959-1524, 2014, Volume 24, Issue 3, pp. 172 - 187

...–Jacobi equation developed.•A link to Hamilton–Jacobi approximation using the expansion approach revealed...

Plantwide processes | Hamilton–Jacobi inequality | Dissipative systems | Decentralized control | Nonlinear process systems | Process networks | Hamilton-Jacobi inequality | FEEDBACK-CONTROL | PASSIVITY-BASED CONTROL | OPERABILITY ANALYSIS | BELLMAN EQUATION | CHEMICAL-PROCESSES | ISAACS EQUATION | ENGINEERING, CHEMICAL | H-INFINITY CONTROL | DISTURBANCE ATTENUATION | DYNAMICAL-SYSTEMS | STATE-FEEDBACK | AUTOMATION & CONTROL SYSTEMS

Plantwide processes | Hamilton–Jacobi inequality | Dissipative systems | Decentralized control | Nonlinear process systems | Process networks | Hamilton-Jacobi inequality | FEEDBACK-CONTROL | PASSIVITY-BASED CONTROL | OPERABILITY ANALYSIS | BELLMAN EQUATION | CHEMICAL-PROCESSES | ISAACS EQUATION | ENGINEERING, CHEMICAL | H-INFINITY CONTROL | DISTURBANCE ATTENUATION | DYNAMICAL-SYSTEMS | STATE-FEEDBACK | AUTOMATION & CONTROL SYSTEMS

Journal Article

Neural Networks, ISSN 0893-6080, 03/2018, Volume 99, pp. 166 - 177

...–Jacobi–Bellman (HJB) equation, Lyapunov technique, and inverse optimality, and hence guarantees that the chaotic drive network synchronizes with the chaotic response network influenced by uncertain noise signals...

Lyapunov technique | Coupled stochastic neural networks | Chaotic synchronization | Noise attenuation | Nonlinear optimal control | Hamilton–Jacobi–Bellman (HJB) equation | CRITERIA | FEEDBACK-CONTROL | SLIDING MODE CONTROL | TIME-VARYING DELAYS | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | EXPONENTIAL LAG SYNCHRONIZATION | Hamilton-Jacobi-Bellman (HJB) equation | SYSTEMS | UNKNOWN-PARAMETERS | Neural networks

Lyapunov technique | Coupled stochastic neural networks | Chaotic synchronization | Noise attenuation | Nonlinear optimal control | Hamilton–Jacobi–Bellman (HJB) equation | CRITERIA | FEEDBACK-CONTROL | SLIDING MODE CONTROL | TIME-VARYING DELAYS | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | EXPONENTIAL LAG SYNCHRONIZATION | Hamilton-Jacobi-Bellman (HJB) equation | SYSTEMS | UNKNOWN-PARAMETERS | Neural networks

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2019, Volume 349, pp. 17 - 44

This paper puts forth a high-order weighted essentially non-oscillatory (WENO) finite-difference scheme to numerically generate the viscosity solution of a new class of Hamilton–Jacobi (HJ...

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Porous elastomers | Flux numerical methods | Electromagnetic solids | Exact Hamilton–Jacobi solutions | High-order WENO schemes | ELECTROELASTIC DEFORMATIONS | VISCOSITY SOLUTIONS | EFFICIENT IMPLEMENTATION | CAVITATION | CLOSED-FORM SOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | DIELECTRIC ELASTOMER COMPOSITES | Exact Hamilton-Jacobi solutions | HOMOGENIZATION | ORDER | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Electromagnetism | Magnetic fields | Electric fields | Analysis | Elastomers | Solid mechanics | Viscosity | Nonlinear equations | Deformation | Particulate composites | Inclusions | Free energy | Domains | Composite materials | Ferrofluids | Runge-Kutta method | Mathematical models | Hamiltonian functions | Finite difference method

Journal Article

Potential Analysis, ISSN 0926-2601, 2/2012, Volume 36, Issue 2, pp. 317 - 337

... ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent, and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup...

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Journal Article

Nonlinear differential equations and applications, ISSN 1420-9004, 2012, Volume 20, Issue 3, pp. 413 - 445

...–Jacobi equations on the network and we study related comparison principles. Under suitable assumptions, we prove in particular that the value function is the unique constrained viscosity solution of the Hamilton...

Networks | Secondary 34H05 | 35F21 | Analysis | Optimal control | Graphs | Mathematics | Hamilton–Jacobi equations | Primary 35R02 | 35Q93 | 49J15 | Viscosity solutions | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | STATE CONSTRAINTS | BELLMAN EQUATIONS | Analysis of PDEs

Networks | Secondary 34H05 | 35F21 | Analysis | Optimal control | Graphs | Mathematics | Hamilton–Jacobi equations | Primary 35R02 | 35Q93 | 49J15 | Viscosity solutions | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | STATE CONSTRAINTS | BELLMAN EQUATIONS | Analysis of PDEs

Journal Article

14.
Full Text
Analysis of the loss of boundary conditions for the diffusive Hamilton–Jacobi equation

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 12/2017, Volume 34, Issue 7, pp. 1913 - 1923

We consider the diffusive Hamilton–Jacobi equation, with superquadratic Hamiltonian, homogeneous Dirichlet conditions and regular initial data. It is known from [4] (Barles–DaLio, 2004...

Loss of boundary conditions | Diffusive Hamilton–Jacobi equation | Viscosity solution | Gradient blow-up | SINGULAR STEADY-STATE | MATHEMATICS, APPLIED | NONLINEAR PARABOLIC EQUATIONS | Diffusive Hamilton-Jacobi equation | GLOBAL-SOLUTIONS

Loss of boundary conditions | Diffusive Hamilton–Jacobi equation | Viscosity solution | Gradient blow-up | SINGULAR STEADY-STATE | MATHEMATICS, APPLIED | NONLINEAR PARABOLIC EQUATIONS | Diffusive Hamilton-Jacobi equation | GLOBAL-SOLUTIONS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 306, pp. 684 - 703

...–Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem...

Nonlinear adjoint methods | Selection problem | Degenerate viscous Hamilton–Jacobi equations | Ergodic problems | AUBRY-MATHER THEORY | VISCOSITY SOLUTIONS | OBSTACLE PROBLEMS | LAGRANGIAN SYSTEMS | LARGE-TIME BEHAVIOR | PRINCIPLES | PDE | MATHEMATICS | CONVEX HAMILTONIANS | PARTIAL-DIFFERENTIAL-EQUATIONS | ADJOINT METHODS | Degenerate viscous Hamilton-Jacobi equations | Sustainable development

Nonlinear adjoint methods | Selection problem | Degenerate viscous Hamilton–Jacobi equations | Ergodic problems | AUBRY-MATHER THEORY | VISCOSITY SOLUTIONS | OBSTACLE PROBLEMS | LAGRANGIAN SYSTEMS | LARGE-TIME BEHAVIOR | PRINCIPLES | PDE | MATHEMATICS | CONVEX HAMILTONIANS | PARTIAL-DIFFERENTIAL-EQUATIONS | ADJOINT METHODS | Degenerate viscous Hamilton-Jacobi equations | Sustainable development

Journal Article

16.
Full Text
Algorithm for Hamilton–Jacobi Equations in Density Space Via a Generalized Hopf Formula

Journal of scientific computing, ISSN 1573-7691, 2019, Volume 80, Issue 2, pp. 1195 - 1239

We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games...

DIMENSIONALITY | MATHEMATICS, APPLIED | Generalized Hopf formula | CURSE | Mean field games | PROJECTIONS | Optimal transport | Hamilton-Jacobi equation in density space | Specific gravity | Algorithms

DIMENSIONALITY | MATHEMATICS, APPLIED | Generalized Hopf formula | CURSE | Mean field games | PROJECTIONS | Optimal transport | Hamilton-Jacobi equation in density space | Specific gravity | Algorithms

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2017, Volume 263, Issue 12, pp. 8418 - 8466

...–Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed...

Stratified structure | Hamilton–Jacobi equations | State constraint problems | Control problem on networks | MATHEMATICS | Hamilton-Jacobi equations | R-N | BELLMAN APPROACH | EIKONAL EQUATIONS | Analysis of PDEs | Mathematics | Optimization and Control

Stratified structure | Hamilton–Jacobi equations | State constraint problems | Control problem on networks | MATHEMATICS | Hamilton-Jacobi equations | R-N | BELLMAN APPROACH | EIKONAL EQUATIONS | Analysis of PDEs | Mathematics | Optimization and Control

Journal Article

Journal of scientific computing, ISSN 1573-7691, 2018, Volume 78, Issue 2, pp. 1023 - 1044

...) schemes for approximating the viscosity solutions to nonlinear Hamilton–Jacobi (HJ) equations. The main difficulty in designing DG schemes lies in the inherent non-divergence form of HJ equations...

Computational Mathematics and Numerical Analysis | Central-upwind scheme | Algorithms | Hamilton–Jacobi equation | Theoretical, Mathematical and Computational Physics | Discontinuous Galerkin scheme | Viscosity solution | Mathematical and Computational Engineering | Mathematics | HERMITE WENO SCHEMES | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCRETIZATION | CENTRAL-UPWIND SCHEMES | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD | Environmental law

Computational Mathematics and Numerical Analysis | Central-upwind scheme | Algorithms | Hamilton–Jacobi equation | Theoretical, Mathematical and Computational Physics | Discontinuous Galerkin scheme | Viscosity solution | Mathematical and Computational Engineering | Mathematics | HERMITE WENO SCHEMES | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | Hamilton-Jacobi equation | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCRETIZATION | CENTRAL-UPWIND SCHEMES | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD | Environmental law

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2016, Volume 219, Issue 2, pp. 793 - 828

... $${S_t u_0}$$ S t u 0 of a Hamilton–Jacobi equation $$u_t+H\big(\nabla_{\!x} u\big)=0, \qquad t\geq 0,\quad x\in\mathbb{R}^N,$$ u t + H ( ∇ x u ) = 0 , t ≥ 0 , x ∈ R N , with a uniformly convex Hamiltonian...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MECHANICS | Environmental law | Conservation laws | Estimates | Numerical methods | Hyperbolic systems | Numerical analysis | Hamilton-Jacobi equation | Mathematical analysis | Texts | Mathematical models

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MECHANICS | Environmental law | Conservation laws | Estimates | Numerical methods | Hyperbolic systems | Numerical analysis | Hamilton-Jacobi equation | Mathematical analysis | Texts | Mathematical models

Journal Article