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Convergence of the optimal values of constrained Markov control processes

Author

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  • Jorge Alvarez-Mena
  • Onésimo Hernández-Lerma

Abstract

We consider a sequence of discounted cost, constrained Markov control processes (CCPs) with countable state space, metric action set and possibly unbounded cost functions. We give conditions under which the sequence of optimal values of the CCPs converges to the optimal value of a limiting CCP, and, furthermore, the accumulation points of sequences of optimal policies for the CCPs are optimal policies for the limiting CCP. These results are obtained via an approximation theorem for general minimization problems. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
    • Handle: RePEc:spr:anresc:v:55:y:2002:i:3:p:461-484
    DOI: 10.1007/s001860200209
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    Cited by:

    1. Héctor Jasso-Fuentes & Tomás Prieto-Rumeau, 2024. "Constrained Markov Decision Processes with Non-constant Discount Factor," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 897-931, August.
    2. Guo, Xianping & Zhang, Wenzhao, 2014. "Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints," European Journal of Operational Research, Elsevier, vol. 238(2), pages 486-496.
    3. Lanlan Zhang & Xianping Guo, 2008. "Constrained continuous-time Markov decision processes with average criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 323-340, April.
    4. Yonghui Huang & Qingda Wei & Xianping Guo, 2013. "Constrained Markov decision processes with first passage criteria," Annals of Operations Research, Springer, vol. 206(1), pages 197-219, July.
    5. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.

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