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We consider a threshold probability optimization problem over controlled Markov chains. The problem is which class of policies we optimize the threshold probability in and how we find an optimal polic...y. This paper formulates the optimization problem in general (large) class and presents a pair of primal and dual methods. A primal method is based upon state-expansion with cumulative rewards up to date and a dual is with threshold levels for the remaining process. We derive duality theorem and consistency theorem, which show that optimal solutions characterize each other. Further a typical model with Bellman and Zadeh's data is illustrated.show more
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KJ00004858589