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A relaxation scheme for Hamilton-Jacobi-Bellman equations. (English) Zbl 1115.65076
Authors’ abstract: We propose a relaxation scheme for solving discrete Hamilton-Jacobi-Bellman equations based on Scheme I of Lions and Mercier. The convergence of the new scheme is established. Numerical example shows the efficiency of the scheme. The existence of the solution of Hamilton-Jacobi-Bellman equation is also discussed.

65K10Optimization techniques (numerical methods)
Full Text: DOI
[1] Lions, P. L.; Mercier, B.: Approximation numerique des equations de Hamilton -- Jacobi -- Bellman, R.A.I.R.O.. Anal. numer. 14, 369-393 (1980) · Zbl 0469.65041
[2] Boulbrachene, M.; Haiour, M.: The finite element approximation of Hamilton -- Jacobi -- Bellman equations. Comput. math. Appl. 41, 993-1007 (2001) · Zbl 0988.65092
[3] Hoppe, R. H. W.: Multigrid method for Hamilton -- Jacobi -- Bellman equations. Numer. math. 49, 239-254 (1986) · Zbl 0577.65088
[4] Sun, M.: Domain decomposition method for solving Hamilton -- Jacobi -- Bellman equations. Numer. funct. Anal. optim. 14, 145-166 (1993) · Zbl 0810.65065
[5] Sun, M.: Alternating direction algorithms for solving Hamilton -- Jacobi -- Bellman equations. Appl. math. Optim. 34, 267-277 (1996) · Zbl 0862.93070
[6] Zhou, S. Z.; Zhan, W. P.: A new domain decomposition method for an HJB equation. J. comput. Appl. math. 159, 195-204 (2003) · Zbl 1034.65052
[7] Young, D.: Iterative solution of large linear systems. (1971) · Zbl 0231.65034