@article{AIHPC_1989__S6__161_0,
author = {Capuzzo Dolcetta, Italo and Falcone, M.},
title = {Discrete dynamic programming and viscosity solutions of the Bellman equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {S6},
year = {1989},
pages = {161-183},
zbl = {0674.49028},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1989__S6__161_0}
}
Capuzzo Dolcetta, I.; Falcone, M. Discrete dynamic programming and viscosity solutions of the Bellman equation. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989) pp. 161-183. http://gdmltest.u-ga.fr/item/AIHPC_1989__S6__161_0/
[1] , A boundary value problem for the minimum time function, to appear on SIAM J. Control and Optimization. | MR 1001919 | Zbl 0682.49034
[2] , , An approximation scheme for the minimum time function, preprint, july 1988 | MR 1051632
[3] , Inéquations quasi-variationnelles du premier ordre et equations d'Hamilton-Jacobi,, C.R.Acad.Sc.Paris,t.296, 1983. | MR 705696
[4] , Deterministic impulse control problems, SIAM J. Control and Optimization, vol.23, 3, 1985 | MR 784578 | Zbl 0571.49020
[5] , , Discontinuous solutions of deterministic optimal stopping time problems, to appear in Math. Methods and Num. Anal. | Numdam | MR 921827
[6] , B.Perthame, Exit time problems in optimal control and vanishing viscosity method, preprint | MR 957658
[7] , Dynamic programming, Princeton University Press, 1957 | MR 90477 | Zbl 0077.13605
[8] , , Applied Dynamic Programming, Princeton University Press, 1962 | MR 140369 | Zbl 0106.34901
[9] , Contrôle stochastique discret, Cahiers du Ceremade
[10] , , An approximation method for stochastic control problems with partial observation of the state-A method for constructing ∈-optimal controls, Acta Applicandae Mathematicae, vol. 10, 2, 1987 | MR 913557 | Zbl 0653.93069
[11] , , Stochastic optimal control: the discrete time case, Academic Press, New York, 1978. | MR 511544 | Zbl 0471.93002
[12] , On a discrete approximation of the Hamilton - Jacobi equation of dynamic programming, Appl.Math.and Optim. 10,1983 | MR 713483 | Zbl 0582.49019
[13] ,, Optimal switching for ordinary differential equations, SIAM J. Control and Optimization, vol.22,1984 | MR 728678 | Zbl 0641.49017
[14] , , Approximate solutions of the Bellman equation of deterministic control theory, Appl. Math.and Optim.11,1984. | MR 743925 | Zbl 0553.49024
[15] , , Hamilton-Jacobi equations and state-constrained problems, to appear in Transactions of the AMS
[16] , , On the dynamic programming inequalities associated with the optimal stopping problem in discrete and continuous time, Numer. Funct. Anal. Optim., 3 (4), 1981. | MR 636737 | Zbl 0476.49021
[17] ,,, On a system of first order quasi-variational inequalities connected with the optimal switching problem, System and Control Letters, Vol.3,No.2,1983. | MR 712129 | Zbl 0521.49008
[18] , , Infinite horizon optimal control, Lecture Notes in Economics and Mathematical Systems, 290, Springer Verlag,1987. | MR 1117222 | Zbl 0649.49001
[19] , , , Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan, vol. 39, 4, 1987 | MR 905626 | Zbl 0644.35016
[20] , , Two approximations of solutions of Hamilton-Jacobi equations, Mathematics of Computation, vol.43, n.167, 1984 | MR 744921 | Zbl 0556.65076
[21] , , Viscosity solutions of Hamilton-Jacobi equations, Trans. A.M.S. 277, 1983. | MR 690039 | Zbl 0599.35024
[22] , An explicit procedure for discretizing continuous optimal control problems, J. Optimization Theory and Applications, 8(1),1971. | MR 311105 | Zbl 0215.21907
[23] , A numerical approach to the infinite horizon problem of deterministic control theory, Appl. Math. Optim. 15, 1987 | MR 866164 | Zbl 0715.49023
[24] , Numerical solution of deterministic continuous control problems, Proceedings International Symposium on Numerical Analysis, Madrid, 1985
[25] , Approximate feedback controls for deterministic control problems, in preparation
[26] , Controlled Markov processes and viscosity solutions of nonlinear evolution equations, Lecture Notes, Scuola Normale Superiore Pisa, to appear | MR 936839 | Zbl 0644.60086
[27] , , Deterministic and stochastic optimal control, Springer Verlag, Berlin, 1975. | MR 454768 | Zbl 0323.49001
[28] , , On deterministic control problems: an approximation procedure for the optimal cost, part I and II, SIAM J. Control and Optimization, vol. 23, n. 2, 1985 | Zbl 0563.49025
[29] , Dynamic programming and Markov processes, Wiley, New York, 1960 | MR 118514 | Zbl 0091.16001
[30] , Necessary and sufficient optimality conditions in the form of Bellman's equation, Soviet Math.Dokl. ,19 (5), 1978. | Zbl 0417.49017
[31] , On nonlinear differential equations, the maximum operation and monotone convergence, J. of Math. and Mech., vol 8, n. 4, 1959 | MR 107731 | Zbl 0092.07703
[32] , Probability methods for approximation in stochastic control and for elliptic equations, Academic Press, New York, 1977 | Zbl 0547.93076
[33] , , Accelerated procedures for the solution of discrete Markov control problems, IEEE Trans. Automatic control, AC-16, 1971 | MR 290841
[34] , , Mathematical programming and the control of Markov chains, Int. J. Control, 13, 1971 | MR 309624 | Zbl 0217.17802
[35] , State increment dynamic programming , American Elsevier, New York, 1967 | MR 233583 | Zbl 0204.47101
[36] , Korsak, A dynamic programming successive approximaton technique with convergence proofs, parts I end II, Automatica, 1969 | Zbl 0199.51001
[37] ,, Foundations of optimal control, J.Wiley, New York, 1967. | MR 220537 | Zbl 0159.13201
[38] , Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. | MR 667669 | Zbl 0497.35001
[39] , Optimal control and viscosity solutions, in I. Capuzzo Dolcetta-W.H. Fleming-T. Zolezzi (Eds.), Recent Mathematical Methods in Dynamic Programming, Lecture Notes in Mathematics 1119, Springer Verlag Berlin, 1985. | MR 790685
[40] , Recent progress on first order Hamilton-Jacobi equations, in Directions in Partial Differential Equations, Academic Press, 1987 | MR 1013837 | Zbl 0659.35015
[41] , , Approximation numérique des equations de Hamilton-Jacobi-Bellman, R.A.I.R.O Analyse numérique, vol.14, n. 4, 1980 | Numdam | MR 596541 | Zbl 0469.65041
[42] , , Differential games, optimal control and directional derivatives of viscosity solutions of Bellman-Isaacs equations, to appear in SIAM J. Control and Optimization | MR 1266104 | Zbl 0569.49019
[43] , Approssimazione di soluzioni viscosità dell'equazione di Bellman, Boll. U.M.I (6), 5-B ,1986. | Zbl 0618.49010
[44] , On convergence of finite difference approximations to optimal control problems for systems with control appearing linearly, Archivum Automatyki i Telemechaniki, 24, Zeszyt 2, 1979. | MR 545656 | Zbl 0408.49038
[45] ,, Relaxation methods in optimal control, to appear in J. Optim. Th. App.
[46] , Probabilistic view of estimates for finite difference methods, to appear in Mathematicae Notae | MR 1049544 | Zbl 0713.60075
[47] , , An algorithm to compute the viscosity solution of the Hamilton-Jacobi-Bellman equation, in C.I. Byrnes, A. Lindquist (eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, 1986 | MR 935396
[48] , , On the convergence of policy iteration in stationary dynamic programming, Math. of Operation Research, vol.4, n. 1, 1979 | MR 543609 | Zbl 0411.90072
[49] , Existence de solution et algorothme de resolutions numeriques de problemes stochastiques degenerées ou non, SIAM J. Control and Optimization, vol.18, 1980 | MR 560048 | Zbl 0439.93057
[50] Optimal control with state space constraint, SIAM J. Control and Optimization, vol.24, 3, 1986 | MR 838056 | Zbl 0597.49023
[51] , Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, Journal of Differential Equations,57,1985. | MR 803085 | Zbl 0536.70020
[52] , Optimal control of differential and functional equations, Academic Press,New York,1972. | MR 372708 | Zbl 0253.49001
[53] , Lectures on the Calculus of Variations and Optimal Control Theory, W.B.Saunders, Philadelfia, 1969. | MR 259704 | Zbl 0177.37801