Duality in Linear Programming Problems Related to Deterministic Long Run Average Problems of Optimal Control

It has been established recently that, under mild conditions, deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPPs) and that these LPPs can be approximated by finite-dimensional LPPs. In this pa...

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Veröffentlicht in:SIAM journal on control and optimization Jg. 47; H. 4; S. 1667 - 1700
Hauptverfasser: Finlay, Luke, Gaitsgory, Vladimir, Lebedev, Ivan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Schlagworte:
Applied mathematics
Approximation
Construction
Grants
Linear programming
Optimization
Production planning
ISSN:0363-0129, 1095-7138
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Abstract It has been established recently that, under mild conditions, deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPPs) and that these LPPs can be approximated by finite-dimensional LPPs. In this paper we introduce the corresponding infinite- and finite-dimensional dual problems and study duality relationships. We also investigate the possibility of using solutions of finite-dimensional LPPs and their duals for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.
AbstractList It has been established recently that, under mild conditions, deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPPs) and that these LPPs can be approximated by finite-dimensional LPPs. In this paper we introduce the corresponding infinite- and finite-dimensional dual problems and study duality relationships. We also investigate the possibility of using solutions of finite-dimensional LPPs and their duals for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.
Author Lebedev, Ivan
Finlay, Luke
Gaitsgory, Vladimir
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  givenname: Ivan
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  fullname: Lebedev, Ivan
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Snippet It has been established recently that, under mild conditions, deterministic long run average problems of optimal control are "asymptotically equivalent" to...
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SubjectTerms Applied mathematics
Approximation
Construction
Grants
Linear programming
Optimization
Production planning
Title Duality in Linear Programming Problems Related to Deterministic Long Run Average Problems of Optimal Control
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