Abstract
This chapter discusses the development of an inverse theorem for a class of infinite-stage dynamic programming problems (main DPs) with one-dimensional state spaces. The chapter presents two related problems to such DPs. One is sub-dynamic programming problem (sub-DP); the other is an inverse problem (inverse DP). The main DP maximizes a generalized total reward under the condition that a generalized total resource is less than or equal to a quantity. Its inverse DP minimizes the generalized total resource under the condition that the generalized total reward is greater than or equal to a quantity. The economic interpretation of the inverse theory of dynamic programming is analogous to that of the duality theory of mathematical programming. The quantities of primal and dual problems in mathematical programming are fixed.
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