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 journalArticlepeer-review

19 Citations (Scopus)
9 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 languageEnglish
Pages (from-to)1667-1700
Number of pages34
JournalSIAM Journal on Control and Optimization
Volume47
Issue number4
DOIs
Publication statusPublished - 2008
Externally publishedYes

Bibliographical note

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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