Analyse de l’algorithme multigrille FMGH de résolution d’équations d’Hamilton-Jacobi-Bellman. (Analysis of the FMGH multigrid algorithm for the solution of the Hamilton-Jacobi-Bellman equations.). (French) Zbl 0712.93069

Akian, Marianne

Analysis and optimization of systems, Proc. 9th Int. Conf., Antibes/Fr. 1990, Lect. Notes Control Inf. Sci. 144, 113-122 (1990).

Summary: [For the entire collection see Zbl 0699.00041.]
The solution of Hamilton-Jacobi-Bellman equations by multgrid methods is studied.The Howard-multigrid algorithm FMGH [cf. the author in: Analysis and optimization of systems, Proc. 8th Int. Conf., Antibes/France 1988, Lect. Notes Control Inf. Sci. 111, 629-640 (1988; Zbl 0682.65077)] is presented and, under some regularity assumptions, a convergence result is established. In addition, it is shown that the complexity of this algorithm is in order of the number of discretization points. Some numerical examples are reported.

MSC:

93E25	Computational methods in stochastic control (MSC2010)
93E20	Optimal stochastic control
65K10	Numerical optimization and variational techniques
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

Hamilton-Jacobi-Bellman equations; multgrid methods; Howard-multigrid algorithm

Citations:

Zbl 0699.00041; Zbl 0682.65077