Optimal control in infinite horizon problems: a Sobolev space approach

Abstract

In this paper, we make use of the Sobolev space W{1,1}ℝ+, ℝn to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L 1 spaces have natural positive cones with no interior points. © Springer-Verlag 2007.