Sufficient conditions for infinite-horizon calculus of variations problems

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		279 - 292
DOI		10.1051/cocv:2000111

DOI: 10.1051/cocv:2000111

ESAIM: COCV, June 2000, Vol. 5, 279-292

Sufficient conditions for infinite-horizon calculus of variations problems

Joël Blot
CERMSEM, M.S.E., Université de Paris 1 Panthéon-Sorbonne, 106-112 boulevard de l'H $\hat{\rm o}$ pital, 75647 Paris Cedex 13, France; (blot@univ-paris1.fr)

Naïla Hayek
L.I.B.R.E., Faculté de Droit et des Sciences Économiques, Université de Franche-Comté, avenue de l'Observatoire, 25030 Besançon Cedex, France, and CERMSEM, M.S.E., Université de Paris 1 Panthéon - Sorbonne, 106-112 boulevard de l'Hôpital, 75647 Paris Cedex 13, France; (hayek@univ-paris1.fr)

Received October 29, 1998. Revised December 9, 1999 and April 17, 2000.

Abstract: After a brief survey of the literature about sufficient conditions, we give different sufficient conditions of optimality for infinite-horizon calculus of variations problems in the general (non concave) case. Some sufficient conditions are obtained by extending to the infinite-horizon setting the techniques of extremal fields. Others are obtained in a special case of reduction to finite horizon. The last result uses auxiliary functions. We treat five notions of optimality. Our problems are essentially motivated by macroeconomic optimal growth models.

Keywords and phrases: Calculus of variations, infinite-horizon problems, optimal growth theory.

AMS Subject Classification: 90A16, 49K99.

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