Capuo Dolcetta, I. On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. (English) Zbl 0582.49019 Appl. Math. Optimization 10, 367-377 (1983). Author’s abstract: An approximation of the Hamilton-Jacobi-Bellman equation connected with the infinite horizon optimal control problem with discount is proposed. The approximate solutions are shown to converge uniformly to the viscosity solution, in the sense of Crandall-Lions, of the original problem. Moreover, the approximate solutions are interpreted as value functions of some discrete-time control problem. This allows to construct by dynamic programming a minimizing sequence of piecewise constant controls. Reviewer: M.Armsen Cited in 3 ReviewsCited in 55 Documents MSC: 49L99 Hamilton-Jacobi theories 49L20 Dynamic programming in optimal control and differential games 49M99 Numerical methods in optimal control 90C39 Dynamic programming Keywords:Hamilton-Jacobi-Bellman equation; infinite-horizon optimal control problem with discount; approximate solutions; viscosity solution; minimizing sequence PDF BibTeX XML Cite \textit{I. Capuo Dolcetta}, Appl. Math. Optim. 10, 367--377 (1983; Zbl 0582.49019) Full Text: DOI OpenURL References: [1] Bertsekas DP, Shreve SE (1978) Stochastic optimal control: The discrete time case. Academic Press, New York · Zbl 0471.93002 [2] Capuzzo Dolcetta I, Evans LC (to appear) Optimal switching for ordinary differential equations. SIAM J Control · Zbl 0641.49017 [3] Capuzzo Dolcetta I, Matzeu M (1981) On the dynamic programming inequalities associated with the deterministic optimal stopping problem in discrete and continuous time. Num Funct Anal Optim 3:425-450 · Zbl 0476.49021 [4] Capuzzo Dolcetta I, Matzeu M, Menaldi JL (to appear) On a system of first order quasi-variational inequalities connected with the optimal switching problem. Systems and Control Letters · Zbl 0521.49008 [5] Crandall MG, Evans LC, Lions PL (to appear) Some properties of the viscosity solutions of Hamilton-Jacobi equations. Trans Amer Math Soc [6] Crandall MG, Lions PL (to appear) Viscosity solutions of Hamilton-Jacobi equations. Trans Amer Math Soc [7] Evans LC (1980) On solving certain nonlinear partial differential equations by accretive operator methods. Israel J Math 36:365-389 · Zbl 0454.35038 [8] Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer-Verlag, Berlin-Heidelberg-New York [9] Gawronski M (1982) Dissertation. Istituto Matematico, Università di Roma, Rome [10] Goletti F (1981) Dissertation. Istituto Matematico, Università di Roma, Rome [11] Henrici P (1962) Discrete variable methods in ordinary differential equations. J. Wiley, New York · Zbl 0112.34901 [12] Lions PL (1982) Generalized solutions of Hamilton-Jacobi equations. Pitman, London · Zbl 0497.35001 [13] Menaldi JL (1982) Le problème de temps d’arret optimal déterministe et l’inéquation variationnelle du premier ordre associée. Appl Math Optim 8:131-158 · Zbl 0486.49005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.