Constrained optimal impulse control and inventory model

Abstract

In this article, we consider the deterministic impulsively controlled system with infinite horizon and several discounted objective functionals. The constructed optimal control problem with functional constraints is reformulated as a Markov decision process, leading to (primal) convex and linear programs in the space of so-called occupation measures. We construct the dual programs and investigate the solvability of all the programs. Example of an inventory model illustrates the developed theory.