Infinite Horizon Optimization is the study of infinite stage stochastic and deterministic mathematical programs. This subsumes a rich and important class of applications including production and inventory control, equipment replacement, optimal search and capacity expansion. Within the framework of an infinite dimensional linear space, this project will: (1) employ best approximations from finite horizon optimal solutions to force convergence to an infinite horizon optimum, and (2) construct a theory of duality for the doubly infinite case to establish necessary and sufficient conditions for infinite horizon optimality and finite horizon optimal convergence.
