Constrained Markov control processes with randomized discounted cost criteria: infinite linear programming approach |
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Authors: | Juan González‐Hernández Raquiel R. López‐Martínez J. Adolfo Minjárez‐Sosa J. Rigoberto Gabriel‐Arguelles |
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Affiliation: | 1. Departamento de Probabilidad y Estadística, IIMAS‐UNAM, , 01000 México D.F., Mexico;2. Facultad de Matemáticas, Universidad Veracruzana, , 91090 Xalapa Ver., Mexico;3. Departamento de Matemáticas, Universidad de Sonora, , Sonora, Mexico |
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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. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | constrained Markov control processes discounted cost random rate infinite linear programming |
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