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We formulate and study the infinite dimensional linear programming (LP)problem associated with the deterministic discrete time long-run averagecriterion optimal control problem. Along with its dual, this LP problem allowsone to characterize the optimal value of the optimal control problem. Thenovelty of our approach is that we focus on the general case wherein theoptimal value may depend on the initial condition of the system.

LP Formulations of Discrete Time Long-Run Average Optimal Control Problems: The Non-Ergodic Case