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Articles

LP-related representations of Cesàro and Abel limits of optimal value functions

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Pages 1151-1170 | Received 28 Jan 2021, Accepted 24 Jul 2021, Published online: 09 Aug 2021
 

Abstract

We consider infinite horizon optimal control problems with time averaging and time discounting criteria and derive linear programming-related representations of Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We show that Cesàro and Abel limits are equal if they are continuous functions of the initial condition, strengthening previous results that require uniform convergence to ensure this equality. The obtained representations of the limits of value functions are used to derive optimality conditions for the long-run average optimal control problem.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

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