Optimal Control in Infinite Horizon Problems: A Sobolev space approachy

by

Cagri Saglam
Bilkent University

In this paper, we make use of the Sobolev space W^{1,1}(R(+), R^(n)) 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 L¹ spaces have natural positive cones with no interior points.