### Abstract

We consider an infinite horizon discounted optimal control problem and its time discretized approximation, and study the rate of convergence of the approximate solutions to the value function of the original problem. In particular we prove the rate is of order 1 as the discretization step tends to zero, provided a semiconcavity assumption is satisfied. We also characterize the limit of the optimal controls for the approximate problems within the framework of the theory of relaxed controls.

Original language | English |
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Pages (from-to) | 161-181 |

Number of pages | 21 |

Journal | Applied Mathematics & Optimization |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1984 Feb |

Externally published | Yes |

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematics(all)

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## Cite this

Dolcetta, I. C., & Ishii, H. (1984). Approximate solutions of the bellman equation of deterministic control theory.

*Applied Mathematics & Optimization*,*11*(1), 161-181. https://doi.org/10.1007/BF01442176