Conditions d'optimalité et dualité en programmation mathématique

Monique Guignard

Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche (1970)

  • Volume: 14, page 7-62
  • ISSN: 0078-950X

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Guignard, Monique. "Conditions d'optimalité et dualité en programmation mathématique." Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche 14 (1970): 7-62. <http://eudml.org/doc/272654>.

@article{Guignard1970,
author = {Guignard, Monique},
journal = {Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche},
language = {fre},
pages = {7-62},
publisher = {Institut Henri Poincaré - Institut de Statistique de l'Université de Paris},
title = {Conditions d'optimalité et dualité en programmation mathématique},
url = {http://eudml.org/doc/272654},
volume = {14},
year = {1970},
}

TY - JOUR
AU - Guignard, Monique
TI - Conditions d'optimalité et dualité en programmation mathématique
JO - Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche
PY - 1970
PB - Institut Henri Poincaré - Institut de Statistique de l'Université de Paris
VL - 14
SP - 7
EP - 62
LA - fre
UR - http://eudml.org/doc/272654
ER -

References

top
  1. [1] Abadie J. - Problèmes d'optimisation, Institut Blaise Pascal, Paris, 1965. 
  2. [2] Abadie J. - On the Kuhn-Tucker Theorem, Operations Research Center, University of California, Berkeley, ORC 65-18. Zbl0183.22803
  3. [3] Arrow K.J., Enthoven A. C. - Quasi-concave Programming, Econometrica, 29 (1961) 779-800. Zbl0104.14302MR138509
  4. [4] Arrow K.J., Hurwicz L. , Uzawa H. - Constraint qualification in maximization problems, Naval Research Log.Quarterley8(1961) 175-191. Zbl0129.34103MR129481
  5. [5] Altman M. - Stationary points in non-linear programming, Bull. Acad. Polonaise Sci., Ser. Sci. Math. Astr. Phys.12(1964) 29-35. Zbl0123.37302MR164810
  6. [6] Bernholtz B. - A new derivation of the Kuhn-Tucker conditions, Quart. Appl. Math.21(1963) 295-299. Zbl0123.37203MR161745
  7. [7] Charnes A., Cooper W.W., Kortanek K. O. - A duality theorem for convex programs for convex constraints, Bull. Amer. Math. Soc.68(1962) 605-608. Zbl0131.36502MR143654
  8. [8] Cottle R. - Symmetric dual quadratic programs, Quart.Appl. Math.21(1963) 237-243. Zbl0127.36802MR156707
  9. [9] Cottle R. - A theorem of Fritz John in Mathematical Programming, The Rand Corporation, 1963. RM 3858 PR. 
  10. [10] Dorn W.S. - Duality in quadratic programming, Quart. Appl. Math.18(1960) 155-162. Zbl0101.37003MR112751
  11. [11] Dorn W.S. - A duality theorem for convex programs, IBM J. Res. Dev.4(1960) 407-413. Zbl0095.14503MR114672
  12. [12] Dorn W.S. - Self-dual quadratic programs, J. SIAM9 (1961) 51-54. Zbl0104.14403MR120038
  13. [13] Dubovitskiy A. Y., Milyutin A. A. - Extremum problems in the presence of constraints, Zh. Vychisl. Mat. i Mat. Fiz., 5 (1965) 395-453. Zbl0158.33504
  14. [14] Duffin R.J. - Dual programs and minimum cost, J. SIAM10 (1962) 119-123. Zbl0106.13905MR137588
  15. [15] Eisenberg E. - Duality in homogeneous programming, Proc . Am. Math. Soc.12 (1961) 783-787. Zbl0102.15503MR129021
  16. [16] Penchel W. - Convex cones, sets and functions, Princeton University (1953). Zbl0053.12203
  17. [17] Fiacco A.W. - Second order sufficient conditions for weak and strict constrained minima, SIAM J. Appl. Math.16 (1968) 105-108. Zbl0157.49604MR227833
  18. [18] Guignard M. - Conditions d'optimalité en programmation mathématique dans un espace de Banach, C. R. Ac. Sc.267 (1968) 5, 223-225. Zbl0159.48504MR235849
  19. [19] Guignard M. - Generalized Kuhn-Tucker conditions for mathematical programming problems in a Banach space, IBM Data Proc. Div. Report 320-2920. SIAM J. on Control7 . (1969) 232-241. Zbl0182.53101MR252042
  20. [20] Halkin H. - An abstract framework for the theory of process optimization, Bull. Amer. Math. Soc.72 (1966) 677-678. Zbl0142.06703MR199004
  21. [21] Halkin H. - Nonlinear nonconvex programming in an infinite dimensional space, Mathematical Theory of Control, ed. A. V. Balakrishnan, Academic Press, New York, (1967) 10-25. Zbl0223.90032MR263427
  22. [22] Halkin H., Neustadt L.W. - General necessary conditions for optimization problems, Proc. Nat. Acad. Sci.USA56 (1966) 1066-1071. Zbl0154.05701MR204184
  23. [23] Hanson M.A. - A duality theorem in nonlinear programming with nonlinear constraints, Austr. J. Stat.3 (1961) 64-72. Zbl0102.15601MR138508
  24. [24] Huard P. - Dual programs, IBM J. Res. Dev.6 (1962) 137-139. Zbl0116.12403
  25. [25] Huard P. - Programme dual, Math. des Progr. Economiques, Monographies de Recherche operationnelle, 1, 13-17. Zbl0204.19505
  26. [26] John F. - Extremum problems with inequalities as subsidiary conditions, Studies and Essays Interscience Pub. Inc., New York (1948) 187-204. Zbl0034.10503MR30135
  27. [27] Kakutani S. - A generalization of Brouwer fixed point theorem, Duke Math.8 (1941) 418-457. MR4776JFM67.0742.03
  28. [28] Kao R.C. - A note on Lagrangian multipliers, The Rand Corporation, (1963) P 2713-1. 
  29. [29] Kuhn, H.W., Tucker A.W. - Nonlinear programming, Proc, 2nd Berkeley Symposium University of California Press, Berkeley, (1951) 481-492. Zbl0044.05903MR47303
  30. [30] Mangasarian O. L. - Duality in nonlinear programming, Quart. Appl. Math.20 (1962) 300-302. Zbl0113.35703MR141530
  31. [31] Mangasarian O. L., Fromovitz S. - The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, J. Math. An. Appl.17 (1967) 37-47 Zbl0149.16701MR207448
  32. [32] Mangasarian O. L. , Ponstein J. - Minimax and duality in nonlinear programming, J. Math. An. Appl.11 (1965) 504-518. Zbl0131.18601MR183538
  33. [33] Mangasarian O. L. - Pseudo-convex functions, J. SIAM Control3 (1965) 281-290. Zbl0138.15702MR191659
  34. [34] Mc Cormick G.P. - Second order conditions for constrained minima, SIAM J. Appl. Math.15 (1967) 641-652 Zbl0166.15601MR216866
  35. [35] Neustadt L.W. - An abstract variational theory with applications to a broad class of optimization problems, Report of the Electronic Sciences Laboratory, University of Southern California, Los Angeles. Zbl0166.09401
  36. [36] Pallu De La Barriere R. - Compléments à la théorie des multiplicateurs en programmation non linéaire, Revue française de Recherche opérationnelle, 27 (1963) 163-180. 
  37. [37] Phipps C.G. - Maxima and minima under restraint, Amer. Math. Monthly59 (1952) 230-235. Zbl0046.06203MR47097
  38. [38] Ponstein J. - An extension of the min-max theorem, SIAM Review7 (1965) 181-188. Zbl0133.42602MR181473
  39. [39] Pschenicheniy B.N. - Convex programming in a normed space, Kibernetika5 (1965) 46-54. Zbl0223.49024
  40. [40] Raffin C. - Programmation mathématique et dualité, Université de Poitiers, Séminaire de Statistiques et Econométrie (1966) 
  41. [41] Rice D. R., Thomas M.E. - Sufficiency conditions in nonlinear programming, College of Engineering, University of Florida (1967). 
  42. [42] Ritter K. - Duality for nonlinear programming in a Banach space, SIAM J. Appl. Math.15 (1967) 294-302. Zbl0152.18404MR216867
  43. [43] Rubinov A.M. - Necessary conditions for an extreme value and their use in the study of certain equations, Soviet Math. Dokl. (trad. angl.) 7 (1966) 978-980. Zbl0185.22603
  44. [44] Russel D. L. - The Kuhn-Tucker conditions in Banach space with an application to control theory, J. Math. An. Appl.15 (1966) 200-212. Zbl0158.10102MR201208
  45. [45] Simmonard M. - Programmation linéaire, Dunod, Paris (1962). Zbl0115.37902
  46. [46] Sion - Sur une généralisation du théorème du minimax, C. R. Ac. Sci.Paris244 (1957) 2120 
  47. [47] Slater - Lagrange multipliers revisited, The Rand Corporation, (1951) RM 676 
  48. [48] Stoer J. - Duality in nonlinear programming and the minmax theorem, Num. Math.5 (1963) 371-379. Zbl0152.38104MR172719
  49. [49] Uzawa H. - The Kuhn-Tucker theorem in concave programming, Studies in linear and nonlinear programming, Stanford University Press, 32-37. 
  50. [50] Vajda - Dans Nonlinear Programming, North Holland Pub. Amsterdam (1966). 
  51. [51] Varaiya P.P. - Nonlinear programming in Banach space, SIAM J. Appl. Math.15 (1967) 284-293. Zbl0171.18004MR218121
  52. [52] Varaiya P. P. - Nonlinear programming and optimal control, ERL Technical Memorandum M-129, University of California, Berkeley (1965). 
  53. [53] Wilde D. J. - Differential calculus in nonlinear programming, Opns. Res. 10 (1962) 764-773. Zbl0112.12204MR147302
  54. [54] Whinston A. - Conjugate functions and dual programs, Nav. Res. Log. Quart.12 (1965) 315-322. Zbl0171.40801MR209009
  55. [55] Wolfe P. - A duality theorem for nonlinear programming, The Rand Corporation, P 2028. Zbl0109.38406

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