On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations

DOI10.1051/m2an:2002002zbMath0998.65067OpenAlexW2098745223MaRDI QIDQ4531296

Publication date: 29 May 2002

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2002__36_1_33_0

zbMATH Keywords

convergence Hamilton-Jacobi-Bellman equation dynamic programming finite difference method viscosity solution approximation monotone approximation schemes

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Dynamic programming in optimal control and differential games (49L20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (82)

On the Rate of Convergence of Finite-Difference Approximations for Elliptic Isaacs Equations in Smooth Domains ⋮ On finite-difference approximations for normalized Bellman equations ⋮ The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures ⋮ Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks ⋮ Convergence of Implicit Schemes for Hamilton--Jacobi--Bellman Quasi-Variational Inequalities ⋮ Uniform Assymptotics in the Average Continuous Control of Piecewise Deterministic Markov Processes : Vanishing Approach ⋮ SIR epidemics with state-dependent costs and ICU constraints: a Hamilton-Jacobi verification argument and dual LP algorithms ⋮ On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients ⋮ Linearization techniques for controlled piecewise deterministic Markov processes; application to Zubov's method ⋮ A fast algorithm for the two dimensional HJB equation of stochastic control ⋮ Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations ⋮ Stochastic control with rough paths ⋮ Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations ⋮ Probabilistic error analysis for some approximation schemes to optimal control problems ⋮ Convergence rates of Markov chain approximation methods for controlled diffusions with stopping ⋮ Hamilton-Jacobi equations for optimal control on multidimensional junctions with entry costs ⋮ High-order filtered schemes for time-dependent second order HJB equations ⋮ Convergence Rate of an Explicit Finite Difference Scheme for a Credit Rating Migration Problem ⋮ (Almost) everything you always wanted to know about deterministic control problems in stratified domains ⋮ On the LP formulation in measure spaces of optimal control problems for jump-diffusions ⋮ Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations ⋮ Stochastic viscosity approximations of Hamilton–Jacobi equations and variance reduction ⋮ Discrete‐time approximation for stochastic optimal control problems under the G‐expectation framework ⋮ Some applications of linear programming formulations in stochastic control ⋮ Error estimation for second‐order <scp>partial differential equations</scp> in nonvariational form ⋮ Numerical analysis of strongly nonlinear PDEs ⋮ Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces ⋮ Continuity of cost in Borkar control topology and implications on discrete space and time approximations for controlled diffusions under several criteria ⋮ Approximate Q Learning for Controlled Diffusion Processes and Its Near Optimality ⋮ Linear Convergence of a Policy Gradient Method for Some Finite Horizon Continuous Time Control Problems ⋮ ERROR ESTIMATES FOR A CLASS OF FINITE DIFFERENCE-QUADRATURE SCHEMES FOR FULLY NONLINEAR DEGENERATE PARABOLIC INTEGRO-PDES ⋮ A probabilistic numerical method for fully nonlinear parabolic PDEs ⋮ A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation ⋮ Subsolutions that are close in the uniform norm are close in the Sobolev norm as well ⋮ Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems ⋮ Outperforming the market portfolio with a given probability ⋮ On the Root Solution to the Skorokhod Embedding Problem Given Full Marginals ⋮ Convergence Rate Estimates for Aleksandrov's Solution to the Monge--Ampère Equation ⋮ Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method ⋮ On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations ⋮ Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions ⋮ On the structure of multifactor optimal portfolio strategies ⋮ Continuous dependence results for non-linear Neumann type boundary value problems ⋮ Abel-type results for controlled piecewise deterministic Markov processes ⋮ A piecewise deterministic Markov toy model for traffic/maintenance and associated Hamilton-Jacobi integrodifferential systems on networks ⋮ Large time behavior for some nonlinear degenerate parabolic equations ⋮ The non-locality of Markov chain approximations to two-dimensional diffusions ⋮ Mayer and optimal stopping stochastic control problems with discontinuous cost ⋮ A stochastic approximation for fully nonlinear free boundary parabolic problems ⋮ Stochastic optimal control and linear programming approach ⋮ An approximation scheme for stochastic controls in continuous time ⋮ Dynamic portfolio selection with nonlinear transaction costs ⋮ Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation ⋮ Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes ⋮ ON THE RATE OF CONVERGENCE OF APPROXIMATION SCHEMES FOR BELLMAN EQUATIONS ASSOCIATED WITH OPTIMAL STOPPING TIME PROBLEMS ⋮ Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations ⋮ Error estimates for numerical approximation of Hamilton-Jacobi equations related to hybrid control systems ⋮ Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems ⋮ Continuous dependence estimates for viscosity solutions of integro-PDEs ⋮ Implications of a regime-switching model on natural gas storage valuation and optimal operation ⋮ Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions ⋮ An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians ⋮ Error Estimates of Penalty Schemes for Quasi-Variational Inequalities Arising from Impulse Control Problems ⋮ Existence of asymptotic values for nonexpansive stochastic control systems ⋮ On the rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman's equations ⋮ Some non monotone schemes for Hamilton-Jacobi-Bellman equations ⋮ Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains ⋮ A viscoelastic model with non-local damping application to the human lungs ⋮ On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients ⋮ NUMERICAL SOLUTIONS FOR THE CHERIDITO-SONER-TOUZI SUPER-REPLICATION MODEL UNDER GAMMA CONSTRAINTS ⋮ Semi-Lagrangian schemes for linear and fully non-linear diffusion equations ⋮ Large-time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN ⋮ Asymptotic Control for a Class of Piecewise Deterministic Markov Processes Associated to Temperate Viruses ⋮ Rate of convergence of finite difference approximations for degenerate ordinary differential equations ⋮ Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source teams ⋮ A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators ⋮ Dynamic programming and error estimates for stochastic control problems with maximum cost ⋮ Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks ⋮ Error estimates for approximations of nonlinear uniformly parabolic equations ⋮ On quadratic approximations for Hamilton-Jacobi-Bellman equations ⋮ Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets ⋮ Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations

Cites Work

This page was built for publication: On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations