Sufficient conditions for infinite-horizon calculus of variations problems

Joël Blot; Naïla Hayek

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 279-292
  • ISSN: 1292-8119

How to cite

top

Blot, Joël, and Hayek, Naïla. "Sufficient conditions for infinite-horizon calculus of variations problems." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 279-292. <http://eudml.org/doc/90571>.

@article{Blot2000,
author = {Blot, Joël, Hayek, Naïla},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal growth theory; infinite horizon problems; sufficient conditions of optimality; techniques of extremal fields},
language = {eng},
pages = {279-292},
publisher = {EDP Sciences},
title = {Sufficient conditions for infinite-horizon calculus of variations problems},
url = {http://eudml.org/doc/90571},
volume = {5},
year = {2000},
}

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
PB - EDP Sciences
VL - 5
SP - 279
EP - 292
LA - eng
KW - optimal growth theory; infinite horizon problems; sufficient conditions of optimality; techniques of extremal fields
UR - http://eudml.org/doc/90571
ER -

References

top
  1. [1] V.M. Alexeev, V.M. Tikhomirov and S.V. Fomin, Commande optimale, French translation. Mir, Moscow ( 1982). MR728225
  2. [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). Zbl0193.20302MR235876
  3. [3] J. Blot and P. Cartigny, Optimality in Infinite-Horizon Problems under Signs Conditions. J. Optim. Theory Appl. (to appear). Zbl1004.49014
  4. [4] J. Blot and N. Hayek, Second-Order Necessary Conditions for the Infinite-Horizon Variational Problems. Math. Oper. Res. 21 ( 1996) 979-990. Zbl0868.90017MR1419912
  5. [5] J. Blot and Ph. Michel, First-Order Necessary Conditions for the Infinite-Horizon Variational Problems. J. Optim. Theory Appl. 88 ( 1996) 339-364. Zbl0843.49014MR1373098
  6. [6] N. Bourbaki, Fonctions d'une variable réelle. Hermann, Paris ( 1976). MR580296
  7. [7] D.A. Carlson, A.B. Haurie and A. Leizarowitz, Infinite Horizon Optimal Control, Deterministic and Stochastic Systems, Second Edition. Springer-Verlag, Berlin ( 1991). Zbl0758.49001
  8. [8] H. Cartan, Calcul Différentiel, Hermann, Paris ( 1967). Zbl0156.36102MR223194
  9. [9] L. Cesari, Optimization Theory and Applications: Problems with Ordinary Differential Equations. Springer-Verlag, New York ( 1983). Zbl0506.49001MR688142
  10. [10] J. Dugundji, Topology. Allyn and Bacon, Boston ( 1966). Zbl0144.21501MR193606
  11. [11] G.E. Ewing, Calculus of Variations, with Applications. Dover Pub. Inc., New York ( 1985). Zbl0198.44501MR807362
  12. [12] W.H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control. Springer-Verlag, New York ( 1975). Zbl0323.49001MR454768
  13. [13] W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York ( 1993). Zbl0773.60070MR1199811
  14. [14] M. Giaquinta and S. Hildebrandt, Calculus of Variations ISpringer-Verlag, Berlin ( 1996). Zbl0853.49001
  15. [15] C. Godbillon, Éléments de topologie algébrique. Hermann, Paris ( 1971). Zbl0218.55001MR301725
  16. [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. Zbl0832.49013MR1343211
  17. [17] M.H. Hestenes, Calculus of Variations and Optimal Control Theory. Robert E. Krieger Publ. Comp., Huntington, N.Y. ( 1980). Zbl0481.49001MR601775
  18. [18] G. Leitman and H. Stalford, A Sufficiency Theorem for Optimal Control. J. Optim. Theory Appl. VIII ( 1971) 169-174. Zbl0208.17306MR300185
  19. [19] D. Leonard and N.V. Long, Optimal Control Theory and Static Optimization in Economics. Cambridge University Press, New York ( 1992). MR1153412
  20. [20] O.L. Mangasarian, Sufficient Conditions for the Optimal Control of Nonlinear Systems. SIAM J. Control IV ( 1966) 139-152. Zbl0154.10401MR189864
  21. [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. Zbl0273.49012MR319007
  22. [22] L. Pontryagin, V. Boltyanskii, R. Gramkrelidze and E. Mitchenko, Théorie Mathématique des Processus Optimaux, French Edition. Mir, Moscow ( 1974). 
  23. [23] H. Sagan, Introduction to the Calculus of Variations. McGraw-Hill, New York ( 1969). 
  24. [24] Th. Sargent, Macroeconomic Theory, Second Edition. Academic Press, New York ( 1986). Zbl0464.90002MR937259
  25. [25] A. Seierstadand K. Sydsaeter, Sufficient Conditions in Optimal Control Theory, Internat. Econom. Rev. 18 ( 1977). Zbl0392.49010MR454795
  26. [26] L. Schwartz, Cours d'Analyse de l'École Polytechnique, Tome 1. Hermann, Paris ( 1967). 
  27. [27] L. Schwartz, Topologie Générale et Analyse Fonctionnelle. Hermann, Paris ( 1970). Zbl0206.06301MR467223
  28. [28] G. Sorger, Sufficient Conditions for Nonconvex Control Problems with State Constraints. J. Optim. Theory Appl. 62 ( 1989) 289-310. Zbl0651.49009MR1009070
  29. [29] J.L. Troutman, Variational Calculus with Elementary Convexity. Springer-Verlag, New York ( 1983). Zbl0523.49001MR697723
  30. [30] V. Zeidan, First and Second Order Sufficient Conditions for Optimal Control and Calculus of Variations. Appl. Math. Optim. 11 ( 1984) 209-226. Zbl0558.49006MR748180
  31. [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. Zbl0868.49001MR1443006

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.