### Abstract

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual, the latter taking the form of a certain max-min problem. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and to investigate a way how the latter can be used for the construction of a near optimal control.

Original language | English |
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Pages (from-to) | 1743-1767 |

Number of pages | 25 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 24 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Apr 2019 |

### Keywords

- Discrete systems
- Duality
- Infinite horizon
- Linear programming
- Numerical methods
- Occupational measures
- Optimal control

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## Cite this

Gaitsgory, V., Parkinson, A., & Shvartsman, I. (2019). Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time.

*Discrete and Continuous Dynamical Systems - Series B*,*24*(4), 1743-1767. https://doi.org/10.3934/dcdsb.2018235