Duality in linear programming problems related to deterministic long run average problems of optimal control

Luke Finlay; Vladimir Gaitsgory; Ivan Lebedev

doi:10.1137/060676398

Duality in linear programming problems related to deterministic long run average problems of optimal control

Luke Finlay^*, Vladimir Gaitsgory, Ivan Lebedev

^*Corresponding author for this work

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

22 Citations (Scopus)

90 Downloads (Pure)

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 finitedimensional LPPs and their duals for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.

Original language	English
Pages (from-to)	1667-1700
Number of pages	34
Journal	SIAM Journal on Control and Optimization
Volume	47
Issue number	4
DOIs	https://doi.org/10.1137/060676398
Publication status	Published - 2008
Externally published	Yes

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Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.

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AU - Gaitsgory, Vladimir

AU - Lebedev, Ivan

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PY - 2008

Y1 - 2008

N2 - 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 finitedimensional LPPs and their duals for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.

AB - 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 finitedimensional 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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IS - 4

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Duality in linear programming problems related to deterministic long run average problems of optimal control

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