### 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 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Mathematics(all)

### Cite this

*Applied Mathematics & Optimization*,

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

**Approximate solutions of the bellman equation of deterministic control theory.** / Dolcetta, I. Capuzzo; Ishii, H.

Research output: Contribution to journal › Article

*Applied Mathematics & Optimization*, vol. 11, no. 1, pp. 161-181. https://doi.org/10.1007/BF01442176

}

TY - JOUR

T1 - Approximate solutions of the bellman equation of deterministic control theory

AU - Dolcetta, I. Capuzzo

AU - Ishii, H.

PY - 1984/2

Y1 - 1984/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34250115257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250115257&partnerID=8YFLogxK

U2 - 10.1007/BF01442176

DO - 10.1007/BF01442176

M3 - Article

AN - SCOPUS:34250115257

VL - 11

SP - 161

EP - 181

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

IS - 1

ER -