Programmes linéaires d'appui d'un programme convexe, application aux conditions d'optimalité et à la dualité
Raffin, Cl.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 2 (1968), p. 27-60 / Harvested from Numdam
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@article{M2AN_1968__2_3_27_0,
     author = {Raffin, Cl.},
     title = {Programmes lin\'eaires d'appui d'un programme convexe, application aux conditions d'optimalit\'e et \`a la dualit\'e},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {2},
     year = {1968},
     pages = {27-60},
     mrnumber = {250677},
     zbl = {0177.48104},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/M2AN_1968__2_3_27_0}
}

Raffin, Cl. Programmes linéaires d'appui d'un programme convexe, application aux conditions d'optimalité et à la dualité. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 2 (1968) pp. 27-60. http://gdmltest.u-ga.fr/item/M2AN_1968__2_3_27_0/

[1] Abadie J., On the Kuhn-Tucker theorem, Non-linear programming. A course-North Holland Publishing Compagny, 1967. | MR 218116 | Zbl 0183.22803

[2] Arrow K. J., Hurwicz L. et Uzawa H., Studies in linear and non-linear programming Stanford University Press, California, 1958. | MR 108399 | Zbl 0091.16002

[3] Berge C. et Ghouila-Houri A., Programmes, jeux et réseaux de transport, Dunod, 1962. | MR 192912 | Zbl 0111.17302

[4] Borget G., Sur l'application d'une méthode de dualité à un problème d'optimisation dynamique à critère quadratique. Thèse de Docteur-Ingénieur Faculté des Sciences,de Caen, 1966.

[5] Bourbaki N., Espaces vectoriels topologiques, Hermann, Paris, 1955.

[6] Charnes A., Cooper W. W., Kortanek K., A duality theorem for convex programs for convex constraints, Bull. Amer, Math. Soc. 63, 1962, 605-608. | MR 143654 | Zbl 0131.36502

[7] Dennis J. B., Mathematical Programming and Electrical Networks, Technology Press and John Wiley and Sons, New York, 1959. | MR 108400

[8] Dorn W. S., A duality theorem for convex programs. IBM J. of Res. Dev. 4, 1960, 407-413. | MR 114672 | Zbl 0095.14503

[9] Duffin R. J., Infinite programs. Linear inequalities and related Systems (edited by Kuhn and Tucker), 1956, 158-170. | MR 87573 | Zbl 0072.37603

[10] Fan K., A generalization of the Alaoglu-Bourbaki theorem and its applications,Math. Zeithschr, 88, 1965, 48-60. | MR 178326 | Zbl 0135.34402

[11] Hanson M. A., A duality theorem in non-linear programming with non linear constraints. Australian J. Statistics, 3, 1961, 64-72. | MR 138508 | Zbl 0102.15601

[12] Huard P., Mathématique des programmes économiques, Monographies de R. O, Dunod, 1961, 13-18. | Zbl 0204.19505

[13] Karlin S., Mathematical methods and theory in games, programming and economies, Addison-Wesley Publishing Compagny, Inc., 1959, vol. I. | MR 1160778

[14] Kuhn H. W. and Tucker A. W., Non-linear programming. Proceedings of the second Berkeley Symposium, University of California Press, 1951, 481-492. | MR 47303 | Zbl 0044.05903

[15] Mangasarian O. L., Duality in non-Linear programming. Quart, Appl. Math., vol. XX, 1962, 300-302. | Zbl 0113.35703

[16] Mangasarian O. L. and Ponstein J., Minimax and duality in non-linear programming, J. of Math. An. and Appl., 11, 1965, 504-518. | MR 183538 | Zbl 0131.18601

[17] Moreau J. J., Fonctionnelles convexes. Séminaire sur les équations aux dérivée partielles, Collège de France, 1966-1967. | Numdam | MR 390443

[18] Pallu De La Barriere R. , Duality in dynamic programming. lst International Conference on programming and control, Colorado Springs, SIAM Journal of Control vol. 4, n° 1, Feb. 1966.

[19] Psenicnyj B. N., Programmation convexe dans un espace normé, Kibernetika (en russe), 1965, 5, 46-54.

[20] Raffin Cl., a) Programmation mathématique et dualité. Séminaire de Statistique de l'Université de Poitiers (mars 1966), publié dans les Cahiers du B.U.R.O. (I.S.U.P.), cahier n° 10, 1-22.

Raffin Cl., b) Comptes rendus de l'Académie des Sciences de Paris, 265, A, 1967, p. 177 et 265, A, 1967, p. 193. | Zbl 0157.49801

Raffin Cl., c) Comptes rendus de l'Académie des Sciences de Paris, 266, A, 1968, p. 766 et 266, A, 1968, p. 839.

[21] Rockafellar R. T., a) Characterization of the subdifferentials of convex functions. Pacific J. of Math., vol. XVII, 1966, 497-510. | MR 193549 | Zbl 0145.15901

Rockafellar R. T.. b) Extension of Fenchel's duality theorem for convex functions, Duke Math. Journal 33-1, March 1966, 81-89. | MR 187062 | Zbl 0138.09301

[22] Stoer J., Duality in non-linear programming and the min-max theorem, Num. Math., 5, 1963, 371-379. | Zbl 0152.38104

[23] Whinston A., Some applications of the conjugate function theory to duality,in [1]. | Zbl 0178.22803

[24] Wolfe P., A duality theorem for non-linear programming, Quart. Appl. Math., 19, 1961, 239-244. | MR 135625 | Zbl 0109.38406