Sufficient conditions for infinite-horizon calculus of variations problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 279-292.
@article{COCV_2000__5__279_0,
     author = {Blot, Jo\"el and Hayek, Na{\"\i}la},
     title = {Sufficient conditions for infinite-horizon calculus of variations problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {279--292},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1765427},
     zbl = {0957.49016},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_2000__5__279_0/}
}
TY  - JOUR
AU  - Blot, Joël
AU  - Hayek, Naïla
TI  - Sufficient conditions for infinite-horizon calculus of variations problems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2000
SP  - 279
EP  - 292
VL  - 5
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/COCV_2000__5__279_0/
LA  - en
ID  - COCV_2000__5__279_0
ER  - 
%0 Journal Article
%A Blot, Joël
%A Hayek, Naïla
%T Sufficient conditions for infinite-horizon calculus of variations problems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2000
%P 279-292
%V 5
%I EDP-Sciences
%U http://archive.numdam.org/item/COCV_2000__5__279_0/
%G en
%F COCV_2000__5__279_0
Blot, Joël; Hayek, Naïla. Sufficient conditions for infinite-horizon calculus of variations problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 279-292. http://archive.numdam.org/item/COCV_2000__5__279_0/

[1] V.M. Alexeev, V.M. Tikhomirov and S.V. Fomin, Commande optimale, French translation. Mir, Moscow ( 1982). | MR

[2] K.J. Arrow, Applications of Control Theory to Economic Growth. Math, of the Decision Sciences, edited by G.B. Dantzig and A.F. Veinott Jr. ( 1968). | MR | Zbl

[3] J. Blot and P. Cartigny, Optimality in Infinite-Horizon Problems under Signs Conditions. J. Optim. Theory Appl. (to appear). | Zbl

[4] J. Blot and N. Hayek, Second-Order Necessary Conditions for the Infinite-Horizon Variational Problems. Math. Oper. Res. 21 ( 1996) 979-990. | MR | Zbl

[5] J. Blot and Ph. Michel, First-Order Necessary Conditions for the Infinite-Horizon Variational Problems. J. Optim. Theory Appl. 88 ( 1996) 339-364. | MR | Zbl

[6] N. Bourbaki, Fonctions d'une variable réelle. Hermann, Paris ( 1976). | MR

[7] D.A. Carlson, A.B. Haurie and A. Leizarowitz, Infinite Horizon Optimal Control, Deterministic and Stochastic Systems, Second Edition. Springer-Verlag, Berlin ( 1991). | Zbl

[8] H. Cartan, Calcul Différentiel, Hermann, Paris ( 1967). | MR | Zbl

[9] L. Cesari, Optimization Theory and Applications: Problems with Ordinary Differential Equations. Springer-Verlag, New York ( 1983). | MR | Zbl

[10] J. Dugundji, Topology. Allyn and Bacon, Boston ( 1966). | MR | Zbl

[11] G.E. Ewing, Calculus of Variations, with Applications. Dover Pub. Inc., New York ( 1985). | MR | Zbl

[12] W.H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control. Springer-Verlag, New York ( 1975). | MR | Zbl

[13] W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York ( 1993). | MR | Zbl

[14] M. Giaquinta and S. Hildebrandt, Calculus of Variations ISpringer-Verlag, Berlin ( 1996). | Zbl

[15] C. Godbillon, Éléments de topologie algébrique. Hermann, Paris ( 1971). | MR | Zbl

[16] R.F. Hartl, S.P. Sethi and R.G. Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints. SIAM Rev. 37 ( 1995) 181-218. | MR | Zbl

[17] M.H. Hestenes, Calculus of Variations and Optimal Control Theory. Robert E. Krieger Publ. Comp., Huntington, N.Y. ( 1980). | MR | Zbl

[18] G. Leitman and H. Stalford, A Sufficiency Theorem for Optimal Control. J. Optim. Theory Appl. VIII ( 1971) 169-174. | MR | Zbl

[19] D. Leonard and N.V. Long, Optimal Control Theory and Static Optimization in Economics. Cambridge University Press, New York ( 1992). | MR

[20] O.L. Mangasarian, Sufficient Conditions for the Optimal Control of Nonlinear Systems. SIAM J. Control IV ( 1966) 139-152. | MR | Zbl

[21] Z. Nehari, Sufficient Conditions in the Calculus of Variations and in the Theory of Optimal Control. Proc. Amer. Math. Soc. 39 ( 1973) 535-539. | MR | Zbl

[22] L. Pontryagin, V. Boltyanskii, R. Gramkrelidze and E. Mitchenko, Théorie Mathématique des Processus Optimaux, French Edition. Mir, Moscow ( 1974).

[23] H. Sagan, Introduction to the Calculus of Variations. McGraw-Hill, New York ( 1969).

[24] Th. Sargent, Macroeconomic Theory, Second Edition. Academic Press, New York ( 1986). | MR | Zbl

[25] A. Seierstadand K. Sydsaeter, Sufficient Conditions in Optimal Control Theory, Internat. Econom. Rev. 18 ( 1977). | MR | Zbl

[26] L. Schwartz, Cours d'Analyse de l'École Polytechnique, Tome 1. Hermann, Paris ( 1967).

[27] L. Schwartz, Topologie Générale et Analyse Fonctionnelle. Hermann, Paris ( 1970). | MR | Zbl

[28] G. Sorger, Sufficient Conditions for Nonconvex Control Problems with State Constraints. J. Optim. Theory Appl. 62 ( 1989) 289-310. | MR | Zbl

[29] J.L. Troutman, Variational Calculus with Elementary Convexity. Springer-Verlag, New York ( 1983). | MR | Zbl

[30] V. Zeidan, First and Second Order Sufficient Conditions for Optimal Control and Calculus of Variations. Appl. Math. Optim. 11 ( 1984) 209-226. | MR | Zbl

[31] A.J. Zaslavski, Existence and Structure of Optimal Solutions of Variational Problems, Recent Developments in Optimization Theory and Nonlinear Analysis, edited by Y. Censor and S. Reich. Amer. Math. Soc. Providence, Rhode Island ( 1997) 247-278. | MR | Zbl