Approximations of Dynamic Programs, II

This paper extends a procedure for approximating dynamic programs due to Fox (Fox, B. L. 1971. Finite-state approximations to denumerable-state dynamic programs. J. Math. Anal. Appl.34 665–670.). Here, the monotone contraction operator model of Denardo (Denardo, E. V. 1967. Contraction mappings in the theory underlying dynamic programming. SIAM Rev.9 165–177.) is approximated by replacing the state space with a subset and defining two approximate local income functions so that the two associated approximate optimal return functions serve as lower and upper bounds for the optimal return function in the original model. Conditions are also given implying convergence of a sequence of approximate optimal return functions to the optimal return function in the original model.