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In this paper, we investigate dynamic programming models with a discrete time and an infinite horizon. The main purpose is to seek an optimal value and an optimal policy under various conditions. To d...o this, we introduce a modified form of the dynamic model which we call a duality of the dynamic one. Then we show that an optimal value of the original model is equal to the one of the dual model, and that there exists an optimal dual policy for the dual model. Further, in view of the dual model we show that there exists an optimal policy for the original model.show more
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