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Applied Mathematics and Optimization

, Volume 10, Issue 1, pp 367–377 | Cite as

On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming

  • I. Capuzzo Dolcetta
Article

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.

Keywords

Control Problem Approximate Solution System Theory Mathematical Method Dynamic Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc 1983

Authors and Affiliations

  • I. Capuzzo Dolcetta
    • 1
    • 2
  1. 1.Istituto MatematicoUniversità di RomaRomeItaly
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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