Constrained Markov control processes in Borel spaces: the discounted case |
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Authors: | Onésimo Hernández-Lerma Juan González-Hernández |
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Affiliation: | (1) Departamento de Matemáticas, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, México (E-mail: ohernand@math.cinvestav.mx), MX;(2) Departamento de Probabilidad y Estadística, IIMAS-UNAM, A. Postal 20-726, México D.F. 01000, México (E-mail: juan@sigma.iimas.unam.mx), MX |
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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. |
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Keywords: | : Constrained Markov control processes discounted cost criterion infinite– dimensional linear programming. |
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