Alternating direction algorithms for solving Hamilton-Jacobi-Bellman equations

Applied Mathematics and Optimization

Volumn 34, Issue 3, 1996, Pages 267-277

  Sun, M ^a  

^a UNIVERSITY OF ALABAMA   (United States)

Author keywords

Alternating direction methods; Convergence; Dynamic programming; Hamilton Jacobi Bellman equations; Optimal controls

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; DYNAMIC PROGRAMMING; FEEDBACK CONTROL; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

ALTERNATING DIRECTION ALGORITHMS; HAMILTONIAN JACOBI BELLMAN EQUATIONS; OPTIMAL FEEDBACK CONTROL LAW; STANDARD MULTIDIMENSIONAL DIFFUSION MODEL; VALUE FUNCTION;

ALGORITHMS;

EID: 0030296136     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01182626     Document Type: Article

References (14)

1. Bartels RH, Stewart GW (1972) Algorithm 432, solution of the matrix equation AX + XB = C, Comm. ACM 15:820-826
2. Bellman R (1961) Adaptive Control Processes: A Guided Tour, Princeton University Press, New Jersey
3. Douglas J, Rachford HH (1956) On the numerical solution of heat conduction problems in two or three space variables, Trans. Amer. Math. Soc. 82:421-439
4. Duff IS, Erisman A, Reid J (1986) Direct Methods for Sparse Matrices, Clarendon Press, Oxford
5. Kellog RB (1969) A nonlinear alternating direction method, Math. Comp. 23:23-27
6. Kushner HJ, Dupuis PG (1992) Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag, New York
7. Ortega JM, Rheinboldt WC (1970) Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York
8. Peaceman DW, Rachford HH (1955) The numerical solution of parabolic and elliptic differential equations, J. SIAM 3:28-41
9. Smith RA (1968 ) Matrix equation XA + BX = C, SIAM J. Applied Math. 16:198-201
10. Sun M (1990) Numerical solutions of singular stochastic control problems in bounded intervals, Lectures in Applied Mathematics, AMS, 26:619-643
11. Sun M (1990) Iterative algorithms for solving undiscounted Bellman equations, Numer. Func. Anal. Optim. 11:149-166
12. Sun M (1993) Domain decomposition algorithms for solving Hamilton-Jacobi-Bellman equations, Numer. Func. Anal. Optim. 14:145-166
13. Tewarson R (1973) Sparse Matrices, Academic Press, New York
14. Varga RS (1962) Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ