Modified Domain Decomposition Method for Hamilton-Jacobi-Bellman Equations

CHEN Guang-hua; CHEN Guang-ming; DAI Zhi-hua

doi:10.3879/j.issn.1000-0887.2010.12.010

Volume 31 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2010 > 31(12): 1496-1502

CHEN Guang-hua, CHEN Guang-ming, DAI Zhi-hua. Modified Domain Decomposition Method for Hamilton-Jacobi-Bellman Equations[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1496-1502. doi: 10.3879/j.issn.1000-0887.2010.12.010

Citation:

PDF( 355 KB)

Modified Domain Decomposition Method for Hamilton-Jacobi-Bellman Equations

doi: 10.3879/j.issn.1000-0887.2010.12.010

1.
Antai College of Economics & Management, Shanghai Jiaotong University, Shanghai 200052, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-10-28
Publish Date: 2010-12-15

Abstract

Abstract

Amodified domain decom position method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal controls with diffusion models.The convergence theorem was estab lished.Numerical results indicate the efficiency and accuracy of the method.
- optmial control,
- discrete Hamilton-Jacobi-Bellm an equations,
- variational inequality,
- modified domain decom position method,
- convergence

FullText(HTML)

References(16)

References

[1]	Boulbrachene M, Haiour M. The finite element approximation of Hamilton-Jacobi-Bellman equations[J]. Comput Math Appl, 2001, 41(7/8): 993-1007. doi: 10.1016/S0898-1221(00)00334-5
[2]	Lions P L, Mercier B. Approximation numerique des equations de Hamilton-Jacobi-Bellman [J]. RAIRO Anal Numer, 1980, 14(4): 369-393.
[3]	Li W, S Wang. Penalty approach to the HJB equation arising in European stock option pricing with proportional transaction costs[J]. J Optim Theory Appl, 2005, 143(2): 279-293.
[4]	Lions P L. Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations Part 1[J]. Communications in Partial Differential Equations, 1983, 8(10): 1101-1174. doi: 10.1080/03605308308820297
[5]	Bardi M, Capuzzo-Dolcetta J. Optimal Control and Viscosity Solution of Hamilton-Jacobi-Bellman Equations[M]. Boston: Birkhuser, 1997.
[6]	ZHOU Shu-zi, ZHAN Wu-ping. A new domain decomposition method for an HJB equation[J]. Journal of Computational and Applied Mathematics, 2003, 159(1): 195-204. doi: 10.1016/S0377-0427(03)00554-5
[7]	Sun M. Domain decomposition algorithms for solving Hamilton-Jacobi-Bellman equations[J]. Numer Funct Anal Optim, 1993, 14(1/2): 145-166. doi: 10.1080/01630569308816513
[8]	Quarteroni A, Valli A. Domain Decomposition Methods for Partial Differential Equations[M]. New York: Oxford Science, 1999.
[9]	Smith B F, Bjrstad P E, Gropp W. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations[M]. New York: Cambridge University Press, 1996.
[10]	Toselli A, Widlund O. Domain Decomposition Methods-Algorithms and Theory[M]. Springer Series in Computational Mathematics, vol 34. Berlin: Springer, 2004.
[11]	Camilli F, Falcone M, Lanucara P, Seghini A. A domain decomposition method for Bellman equations[C] Keyes D E, Xu J C. Proceedings of DDM 7. AMS, Providence, 1994: 477-484
[12]	Zhou S, Zou Z Y. An iterative algorithm for a quasivariational inequality systemrelated to HJB equation[J]. Journal of Computational and Applied Mathematics, 2008, 219(1): 1-8. doi: 10.1016/j.cam.2007.07.013
[13]	周叔子，陈光华. 解离散HJB方程的一个单调迭代法[J] .应用数学, 2005, 18(4): 639-643.
[14]	Glowinski R, Lions J L, Tremolieres R. Numerical Analysis of Variational Inequalities[M]. Amsterdam: North-Holland, 1981.
[15]	Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holland, 1978.
[16]	Hoppe R H W. Multigrid methods for Hamilton-Jacobi-Bellman equations[J]. Numer Math, 1986, 49(2/3): 239-254. doi: 10.1007/BF01389627