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

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.


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