Sufficient conditions for infinite-horizon calculus of variations problems
CERMSEM, M.S.E., Université de Paris 1
Panthéon-Sorbonne, 106-112 boulevard de l'Hôpital,
75647 Paris Cedex 13, France; email@example.com.
2 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; firstname.lastname@example.org.
Revised: 9 December 1999
Revised: 17 April 2000
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.
Mathematics Subject Classification: 90A16 / 49K99
Key words: Calculus of variations / infinite-horizon problems / optimal growth theory.
© EDP Sciences, SMAI, 2000