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Sufficient conditions for infinite-horizon calculusof variations problems

Published online by Cambridge University Press:  15 August 2002

Joël Blot and
Naïla Hayek
Joël Blot
Affiliation:
CERMSEM, M.S.E., Université de Paris 1 Panthéon-Sorbonne, 106-112 boulevard de l'Hôpital, 75647 Paris Cedex 13, France; blot@univ-paris1.fr.
Naïla Hayek
Affiliation:
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.
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Abstract

After a brief survey of the literature about sufficient conditions, we givedifferent sufficient conditions of optimality for infinite-horizon calculusof variations problems in the general (non concave) case. Some sufficientconditions are obtained by extending to the infinite-horizon setting thetechniques of extremal fields. Others are obtained in a specialqcase of reduction to finite horizon. The last result uses auxiliaryfunctions. We treat five notions of optimality. Our problems are essentiallymotivated by macroeconomic optimal growth models.

Keywords

Calculus of variationsinfinite-horizon problemsoptimal growth theory.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000, pp. 279 - 292
Copyright
© EDP Sciences, SMAI, 2000

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