### 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 (US) |
---|---|

Pages (from-to) | 1743-1767 |

Number of pages | 25 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### 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 › Review article

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

Y1 - 2019/4

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.

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

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

U2 - 10.3934/dcdsb.2018235

DO - 10.3934/dcdsb.2018235

M3 - Review article

AN - SCOPUS:85061837499

VL - 24

SP - 1743

EP - 1767

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 4

ER -