Constrained Markov control processes with randomized discounted cost criteria: infinite linear programming approach

Constrained Markov control processes with randomized discounted cost criteria: infinite linear programming approach

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Article ID: iaor201522432
Volume: 35
Issue: 5
Start Page Number: 575
End Page Number: 591
Publication Date: Sep 2014
Journal: Optimal Control Applications and Methods
Authors: , , ,
Keywords: optimization, markov processes, programming: linear
Abstract:

In this paper, we study constrained Markov control processes on Borel spaces with possibly unbounded one‐stage cost, under a discounted optimality criterion with random discount factor and restrictions of the same kind. We prove that the corresponding optimal control problem is equivalent to an infinite‐dimensional linear programming problem. In addition, considering the dual program, we show that there is no duality gap, and moreover, the strong duality condition holds. Hence, both programs are solvable, and their optimal values coincide.

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