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

Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman

Research output: Contribution to journalReview article

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1743-1767
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number4
DOIs
StatePublished - Apr 2019

Fingerprint

Infinite Horizon
Optimality Conditions
Linear programming
Optimal Control Problem
Discrete-time
Approximate Solution
Min-max Problem
Necessary and Sufficient Optimality Conditions
Optimal Control
Form

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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title = "Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time",
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.",
author = "Vladimir Gaitsgory and Alex Parkinson and Ilya Shvartsman",
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AU - Parkinson, Alex

AU - Shvartsman, Ilya

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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.

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JO - Discrete and Continuous Dynamical Systems - Series B

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