Input optimization for infinite-horizon discounted programs
Let V(x) denote the optimal (maximal) value of a discrete time dynamic program, given the initial state x. This paper is concerned with the inverse correspondence \(V^{-1}\) and its infimum \[ I(v)\quad:=\quad \inf _{x}\{x: V(x)\geq v\} \] for discounted, infinite-horizon programs with one-dimensional state space and monotone V(\(\cdot)\). The function I(v), interpreted as the optimal (minimal) input required to achieve v, is computed using dynamic programming recursion (Theorem 3.1) or value iteration (Theorem 3.2). An application to mathematical economics (optimal consumption plan) is given.
scientific article; zbMATH DE number 4051383