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SIAMCO
2008

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

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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 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. Key words. long run average optimal control, occupational measures, averaging, linear programming, duality AMS subject classifications. 34E15, 34C29, 34A60, 93C70 DOI. 10.1137/060676398
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMCO
Authors Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev
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