Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach |
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Authors: | Cuong Le Van Raouf Boucekkine Cagri Saglam |
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Affiliation: | (1) Centre d’Economie de la Sorbonne, CNRS, UMR 8174, Université de Paris 1 Pantheon-Sorbonne, 106-112 Bd de l’Hopital, 75013 Paris, France;(2) Department of Economics and CORE, Université catholique de Louvain, Place Montesquieu 3, 1348 Louvain-la-Neuve, Belgium;(3) Department of Economics, Bilkent University, 06800 Ankara, Turkey |
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Abstract: | In this paper, we make use of the Sobolev space 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. The paper was written when Cuong Le Van was visiting CORE, Université catholique de Louvain, and Cagri Saglam was a research fellow of the Economics Department of the same university. The authors are indebted to an anonymous referee and Takashi Kamihigashi for very useful comments. R. Boucekkine acknowledges the support of the Belgian research programmes PAI P4/01 and ARC 03/08-302. |
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Keywords: | Optimal control Sobolev spaces Transversality conditions Order ideal |
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