Controlled Markov Set‐chains with Set‐valued Rewards—The Average Case
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説明
<jats:p>In this paper, the average case of finite state controlled Markov set‐chains with <jats:bold>R</jats:bold><jats:sup><jats:italic>p</jats:italic></jats:sup>‐set‐valued rewards are considered. The optimization is done by a pseudo‐order relation on the set of all convex and compact subsets of <jats:bold>R</jats:bold><jats:sup><jats:italic>p</jats:italic></jats:sup> induced by a closed convex cone. We introduce a <jats:italic>v</jats:italic>‐step contractive property (minorization condition) for the average case and by use of this method the average expected reward set from a periodic policy is characterized. And, applying the scalarization technique, a Pareto optimal policy is obtained. Also, a numerical example is given to comprehend our results.</jats:p>
収録刊行物
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- International Transactions in Operational Research
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International Transactions in Operational Research 9 113-123, 2002-01-01
Wiley