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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 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 qcase 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

Calculus of variationsinfinite-horizon problemsoptimal growth theory.
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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