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It has been recently established that a deterministic infinite horizondiscounted optimal control problem in discrete time is closely related to acertain infinite dimensional linear programming problem and its dual. In thepresent paper, we use these results to establish necessary and sufficientoptimality conditions for this optimal control problem and apply them toconstruct a near optimal control.

Linear Programming Based Optimality Conditions and Approximate Solution  of a Deterministic Infinite Horizon Discounted Optimal Control Problem in  Discrete Time