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Monotonicity of minimizers in optimization problems with applications to Markov control processes. (English) Zbl 1170.90513
Summary: Firstly, in this paper there is considered a certain class of possibly unbounded optimization problems on Euclidean spaces, for which conditions that permit to obtain monotone minimizers are given. Secondly, the theory developed in the first part of the paper is applied to Markov Control Processes (MCPs) on real spaces with possibly unbounded cost function, and with possibly noncompact control sets, considering both the discounted and the average cost as optimality criterion. In the context described, conditions to obtain monotone optimal policies are provided. For the conditions of MCPs presented in the article, several controlled models including, in particular, two inventory/production systems and the linear regulator problem are supplied.

90C40 Markov and semi-Markov decision processes
93E20 Optimal stochastic control
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