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

Juan González-Hernández; Raquiel R. López-Martínez; J. Adolfo Minjárez-Sosa; J. Rigoberto Gabriel-Arguelles

doi:10.1002/oca.2089

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

Juan González-Hernández, Raquiel R. López-Martínez, J. Adolfo Minjárez-Sosa^*, J. Rigoberto Gabriel-Arguelles

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	575-591
Number of pages	17
Journal	Optimal Control Applications and Methods
Volume	35
Issue number	5
DOIs	https://doi.org/10.1002/oca.2089
State	Published - Sep 2014

Bibliographical note

Publisher Copyright:
Copyright © 2013 John Wiley & Sons, Ltd.

Keywords

Constrained Markov control processes
Discounted cost
Infinite linear programming
Random rate

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10.1002/oca.2089

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title = "Constrained Markov control processes with randomized discounted cost criteria: Infinite linear programming approach",

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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T2 - Infinite linear programming approach

AU - González-Hernández, Juan

AU - López-Martínez, Raquiel R.

AU - Minjárez-Sosa, J. Adolfo

AU - Gabriel-Arguelles, J. Rigoberto

PY - 2014/9

Y1 - 2014/9

N2 - 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.

AB - 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.

KW - Constrained Markov control processes

KW - Discounted cost

KW - Infinite linear programming

KW - Random rate

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U2 - 10.1002/oca.2089

DO - 10.1002/oca.2089

M3 - Artículo

SN - 0143-2087

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SP - 575

EP - 591

JO - Optimal Control Applications and Methods

JF - Optimal Control Applications and Methods

IS - 5

ER -

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

Abstract

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Keywords

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