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Constrained Markov control processes in Borel spaces: the discounted case

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  • Onésimo Hernández-Lerma
  • Juan González-Hernández

Abstract

We consider constrained discounted-cost Markov control processes in Borel spaces, with unbounded costs. Conditions are given for the constrained problem to be solvable, and also equivalent to an equality-constrained (EC) linear program. In addition, it is shown that there is no duality gap between EC and its dual program EC * , and that, under additional assumptions, also EC * is solvable, so that in fact the strong duality condition holds. Finally, a Farkas-like theorem is included, which gives necessary and sufficient conditions for the primal program EC to be consistent. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Onésimo Hernández-Lerma & Juan González-Hernández, 2000. "Constrained Markov control processes in Borel spaces: the discounted case," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 271-285, November.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:2:p:271-285
    DOI: 10.1007/s001860000071
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    Cited by:

    1. Hernández-Lerma, Onésimo & Romera, Rosario, 2000. "Pareto optimality in multiobjective Markov control processes," DES - Working Papers. Statistics and Econometrics. WS 9865, Universidad Carlos III de Madrid. Departamento de Estadística.

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