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Constrained Markov control processes with randomized discounted cost criteria: infinite linear programming approach
Author(s) -
GonzálezHernández Juan,
LópezMartínez Raquiel R.,
MinjárezSosa J. Adolfo,
GabrielArguelles J. Rigoberto
Publication year - 2013
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2089
Subject(s) - duality (order theory) , mathematics , markov decision process , mathematical optimization , dual (grammatical number) , linear programming , markov chain , optimal control , duality gap , dynamic programming , markov process , weak duality , control (management) , optimization problem , discrete mathematics , computer science , statistics , literature , artificial intelligence , art
SUMMARY 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.