### 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.

Language | English |
---|---|

Pages | 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 |

### Fingerprint

### Keywords

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

### Cite this

*Discrete and Continuous Dynamical Systems - Series B*,

*24*(4), 1743-1767. https://doi.org/10.3934/dcdsb.2018235

}

*Discrete and Continuous Dynamical Systems - Series B*, vol. 24, no. 4, pp. 1743-1767. https://doi.org/10.3934/dcdsb.2018235

**Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time.** / Gaitsgory, Vladimir; Parkinson, Alex; Shvartsman, Ilya.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time

AU - Gaitsgory, Vladimir

AU - Parkinson, Alex

AU - Shvartsman, Ilya

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - Discrete systems

KW - Duality

KW - Infinite horizon

KW - Linear programming

KW - Numerical methods

KW - Occupational measures

KW - Optimal control

UR - http://www.scopus.com/inward/record.url?scp=85061837499&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2018235

DO - 10.3934/dcdsb.2018235

M3 - Article

VL - 24

SP - 1743

EP - 1767

JO - Discrete and Continuous Dynamical Systems - Series B

T2 - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 4

ER -