Discretizing Dynamic Programs.

by Bennett L. Fox

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Procedure for obtaining finite-state approximations to uncountable-state dynamic programs when the state space need not be compact. Except in rare cases, it is necessary to discretize uncountable-state dynamic programs to obtain even an approximate solution. This paper describes a procedure for discretizing dynamic programs which begins by assuming that the state space is compact; a finite grid is constructed so that any point in the space is in the neighborhood of a grid point. The problem is then to find conditions such that the approximations converge to the solution of the original problem as the mesh becomes finer. A two-step approximation procedure is developed for a space that is not compact. The result obtained here complements the analogous result in RM-6195 for denumerable-state programs. 7 pp. Ref.

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