Domain decomposition algorithms for solving Hamilton-Jacobi-Bellman equations. (English) Zbl 0810.65065

A main obstacle in numerical solving Hamilton-Jacobi equations is the large dimension of the discretized problems. As an alternative, this paper presents some domain decomposition based algorithms, which are used to solve some Hamilton-Jacobi-Bellman equations arising in stochastic control problems.


65K10 Numerical optimization and variational techniques
65L05 Numerical methods for initial value problems involving ordinary differential equations
37-XX Dynamical systems and ergodic theory
93E25 Computational methods in stochastic control (MSC2010)
93E03 Stochastic systems in control theory (general)
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[1] Bancora-Imbert M. C., SIAM J. Sci. Statist. Comput 9 pp 970– (1989)
[2] Bellman R., Adaptive Control Processes: A Guided Tour (1961) · Zbl 0103.12901
[3] Bertsekas D. P., IEEE, AC-34 pp 589– (1989)
[4] Chan T.F., Domain Decomposition Methods (1989)
[5] DOI: 10.1007/BF01399311 · Zbl 0478.65062
[6] Fleming W. H., Deterministic and Stochastic Optimal Control (1975) · Zbl 0323.49001
[7] Glowinski R., Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations (1991)
[8] Glowinski, R. and Périaux, J. 1985.Finite element, least squares and domain decomposition methods for numerical solution of nonlinear problems in fluid dynamics, Vol. 1127, 1–114. Berlin: Springer-Verlag. Lecture Notes in Mathematics
[9] Kushner H. J., Probability Methods for Approximations in Stochastic Control and for Elliptic Equations (1977) · Zbl 0547.93076
[10] Lions P. L., Domain Decomposition Methods for Partial Differential Equations pp 1– (1988)
[11] DOI: 10.1007/BF01397683 · Zbl 0154.41201
[12] Schwarz, H. A. 1890, 1870.Gesammelete Mathematische Abhandlungen, Vol. 2, 15, 133, 272–143, 286. Berlin: Springer-Verlag, First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich.
[13] Sun M., Stochastics 21 pp 303– (1987) · Zbl 0628.49017
[14] Sun M., Lectures in Applied Math., AMS 26 pp 619– (1990)
[15] DOI: 10.1080/01630569008816367 · Zbl 0691.49032
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