论文信息 - A numerical algorithm based on a variational iterative approximation for the discrete Hamilton-Jacobi-Bellman (HJB) equation

A numerical algorithm based on a variational iterative approximation for the discrete Hamilton-Jacobi-Bellman (HJB) equation

This paper presents a numerical algorithm based on a variational iterative approximation for the Hamilton-Jacobi-Bellman equation, and a domain decomposition technique based on this algorithm is also studied. The convergence theorems have been established. Numerical results indicate the efficiency and accuracy of the methods.

Guanghua Chen | Guangming Chen

[1] R. Hoppe. Multi-grid methods for Hamilton-Jacobi-Bellman equations , 1986 .

[2] P. Lions,et al. Approximation numérique des équations Hamilton-Jacobi-Bellman , 1980 .

[3] Shuzi Zhou,et al. A new domain decomposition method for an HJB equation , 2003 .

[4] X. Zhou,et al. Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[5] Avner Friedman,et al. Optimal stochastic switching and the Dirichlet problem for the Bellman equation , 1979 .

[6] M. Haiour,et al. The finite element approximation of Hamilton-Jacobi-Bellman equations , 2001 .

[7] M. Sun,et al. Alternating direction algorithms for solving Hamilton-Jacobi-Bellman equations , 1996 .

[8] Kok Lay Teo,et al. Numerical Solution of Hamilton-Jacobi-Bellman Equations by an Upwind Finite Volume Method , 2003, J. Glob. Optim..

[9] P. Forsyth,et al. Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance , 2007 .