Free Access
Issue
ESAIM: M2AN
Volume 29, Number 1, 1995
Page(s) 97 - 122
DOI https://doi.org/10.1051/m2an/1995290100971
Published online 31 January 2017
  1. [A] M. AKIAN, 1990, Analyse de l'algorithme multigrille FMGH de résolution d'équations de Hamilton-Jacobi-Bellman, in A. Bensoussan, J.-L Lions (Eds.), Analysis and Optimization of Systems, Lecture Notes in Control and Information Science, n° 144, Springer-Verlag, 113-122. [MR: 1070728] [Zbl: 0712.93069] [Google Scholar]
  2. [BS] G. BARLES,P. E. SOUGANIDIS, 1991, Convergence of approximation schemes for fully non linear second order equations, Asymptotic Analysis, 4, 271-282. [MR: 1115933] [Zbl: 0729.65077] [Google Scholar]
  3. [BCM] M.-C. BANCORA-IMBERT, P.-L. CHOW, J.-L. MENALDI, 1989, On the numerical approximation of an optimal correction problem, SIAM J. Sci Statist. Comput., 9, 970-991. [MR: 963850] [Zbl: 0661.65150] [Google Scholar]
  4. [BeS] D. P. BERTSEKAS, S. SHREVE, 1978, Stochastic Optimal Control: the discrete time case, Academic Press, New York. [MR: 511544] [Zbl: 0471.93002] [Google Scholar]
  5. [C] I. CAPUZZO-DOLCETTA,, 1983, On a discrete approximation of the Hamilton-Jacobi equation of Dynamic Programming, Appl. Math. Optim., 10, 367-377. [MR: 713483] [Zbl: 0582.49019] [Google Scholar]
  6. [CDF] I. CAPUZZO-DOLCETTA, M. FALCONE, 1989, Discrete dynamic programming and viscosity solution of the Bellman equation, Annales de l'Institut H. Poincaré-Analyse non linéaire, 6, 161-184. [EuDML: 78193] [MR: 1019113] [Zbl: 0674.49028] [Google Scholar]
  7. [CF] F. CAMILLI, M. FALCONE, forthcoming. [Google Scholar]
  8. [CI] I. CAPUZZO-DOLCETTA, H. ISHII, 1984, Approximate solutions of the Bellman equation of Deterministic Control Theory, Appl. Math. Optim., 11, 161-181. [MR: 743925] [Zbl: 0553.49024] [Google Scholar]
  9. [CIL] M. CRANDALL, H. ISHII, P.-L. LIONS, 1991, A user guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27, 1-67. [MR: 1118699] [Zbl: 0755.35015] [Google Scholar]
  10. [FI] M. FALCONE, 1987, 1991, A numerical approach to infinite horizon problem,Appl. Math. Optim., 15, 1-13 and 23, 213-214. [MR: 866164] [Zbl: 0715.49023] [Google Scholar]
  11. [F2] M. FALCONE, 1985, Numerical solution of optimal control problems, Proceedings of the International Symposium on Numerical Analysis, Madrid. [Google Scholar]
  12. [FF] M. FALCONE, R. FERRETTI, 1994, Discrete-time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 67,315-344. [MR: 1269500] [Zbl: 0791.65046] [Google Scholar]
  13. [FIF] B. G. FITZPATRICK, W. H. FLEMING, Numerical Methods for an optimal investment/consumption model, to appear on Math. Operation Research. [MR: 1135050] [Zbl: 0744.90003] [Google Scholar]
  14. [FS] W. H. FLEMING, M. H. SONER, 1993, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York. [MR: 1199811] [Zbl: 0773.60070] [Google Scholar]
  15. [GR] R. GONZALES, E. ROFMAN, 1985, On determmistic control problems : an approximation procedure for the optimal cost(part I and II), SIAM J. Control and Optimization, 23, 242-285. [Zbl: 0563.49025] [Google Scholar]
  16. [H] R. HOPPE, 1986, Multi-grid methods for Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 49, 235-254. [EuDML: 133110] [MR: 848524] [Zbl: 0577.65088] [Google Scholar]
  17. [IL] H. ISHII, P.-L. LIONS, 1990, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Diff. Eq., 83, 26-78. [MR: 1031377] [Zbl: 0708.35031] [Google Scholar]
  18. [K] H. J. KUSHNER, 1977, Probability methods for approximations in stochastic control and for elliptic equations, Academic Press, New York. [MR: 469468] [Zbl: 0547.93076] [Google Scholar]
  19. [KD] H. J. KUSHNER, P. DUPUIS, 1992, Numerical methods for stochastic control problems in continuous time, Springer Verlag, New York. [MR: 1217486] [Zbl: 0754.65068] [Google Scholar]
  20. [Ll] P.-L. LIONS, 1983, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations part 1 the dynamic programming principle and applications, Comm. Partial Diff. Equations, 8, 1101-1174. [MR: 709164] [Zbl: 0716.49022] [Google Scholar]
  21. [L2] P.-L. LIONS, 1983, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations part 2 : Viscosity solutions and uniqueness, Comm. Partial Diff. Equations, 8, 1229-1270. [MR: 709162] [Zbl: 0716.49023] [Google Scholar]
  22. [LM] P.-L. LIONS, B. MERCIER, Approximation numérique des équations de Hamilton-Jacobi-Bellman, RAIRO Anal. Numer., 14, 369-393. [EuDML: 193367] [MR: 596541] [Zbl: 0469.65041] [Google Scholar]
  23. [M] J.-L. MENALDI, 1989, Some estimates for finite difference approximations, SIAM J. Control Optim., 27, 579-607. [MR: 993288] [Zbl: 0684.93088] [Google Scholar]
  24. [Q] J.-P. QUADRAT, 1980, Existence de solution et algorithme de résolutions numériques de problèmes stochastiques dégénérées ou non, SIAM J. Control and Optimization, 18, 199-226. [MR: 560048] [Zbl: 0439.93057] [Google Scholar]
  25. [S] P.-E. SOUGANIDIS, 1985, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Diff. Eq., 57, 1-43. [MR: 803085] [Zbl: 0536.70020] [Google Scholar]
  26. [Su] M. SUN, 1993, Domain decomposition algorithms for solvign Hamilton-Jacobi-Bellman equations, Numerical Func. Anal. and Optim., 14, 145-166. [MR: 1210467] [Zbl: 0810.65065] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you