Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

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Article ID: iaor19942349
Country: Germany
Volume: 39
Start Page Number: 131
End Page Number: 155
Publication Date: Jan 1994
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , ,
Keywords: control
Abstract:

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, the authors study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; the present approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.

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