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

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and apply them to construct a near optimal control.