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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Bibliographic Details
Published in:SIAM journal on control and optimization Vol. 47; no. 4; pp. 1667 - 1700
Main Authors: Finlay, Luke, Gaitsgory, Vladimir, Lebedev, Ivan
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Subjects:
Applied mathematics
Approximation
Construction
Grants
Linear programming
Optimization
Production planning
ISSN:0363-0129, 1095-7138
Online Access:Get full text
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Summary: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.
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ISSN:0363-0129
1095-7138
DOI:10.1137/060676398