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 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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