Geodesic
Deterministic optimal policies for Markov control processes with pathwise constraints
Armando F. Mendoza-Pérez 1   ; Onésimo Hernández-Lerma 2
1 CEFyMAP-UNACH Cuarta Oriente Norte 1428 entre 13 y 14 norte C.P. 29040 Tuxtla Gutiérrez, Chiapas, México
2 Mathematics Department CINVESTAV-IPN A. Postal 14-740 México D.F. 07000, México
Applicationes Mathematicae, Tome 39 (2012) no. 2, pp. 185-209 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to obtain constrained optimal policies as the limit of unconstrained deterministic optimal policies. In addition, we give sufficient conditions for the existence of deterministic policies that solve these constrained problems.
DOI : 10.4064/am39-2-6
Keywords: paper deals discrete time markov control processes borel spaces unbounded rewards under suitable hypotheses randomized stationary policy optimal certain expected constrained problem ecp only optimal corresponding pathwise constrained problem pathwise moreover certain parametric family unconstrained optimality equations yields convergence properties lead approximation scheme which allows obtain constrained optimal policies limit unconstrained deterministic optimal policies addition sufficient conditions existence deterministic policies solve these constrained problems

Armando F. Mendoza-Pérez  1   ; Onésimo Hernández-Lerma  2

1 CEFyMAP-UNACH Cuarta Oriente Norte 1428 entre 13 y 14 norte C.P. 29040 Tuxtla Gutiérrez, Chiapas, México
2 Mathematics Department CINVESTAV-IPN A. Postal 14-740 México D.F. 07000, México 
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     title = {Deterministic optimal policies for
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Armando F. Mendoza-Pérez; Onésimo Hernández-Lerma. Deterministic optimal policies for
 Markov control processes
 with pathwise constraints. Applicationes Mathematicae, Tome 39 (2012) no. 2, pp. 185-209. doi: 10.4064/am39-2-6

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