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In this paper, we consider how to construct the optimal solutions for ageneral discrete time infinite horizon optimal control problem. We establishnecessary and sufficient conditions for optimality in the sense of a modifiedoptimality criterion. We also consider how transversality conditions arerelated to steady states. The results are applied to two examples todemonstrate how the new transversality conditions derived in this paper differfrom those given in the previous literature.

The "Eating up Assumption", Transversality Conditions, and Steady States for Discrete Time Infinite Horizon Problems