@incollection{MSMF_1979__60__57_0, author = {Hiriart-Urruty, J-B.}, title = {New concepts in nondifferentiable programming}, booktitle = {Analyse non convexe (Pau, 1977)}, series = {M\'emoires de la Soci\'et\'e Math\'ematique de France}, pages = {57--85}, publisher = {Soci\'et\'e math\'ematique de France}, number = {60}, year = {1979}, doi = {10.24033/msmf.261}, mrnumber = {81a:90138}, zbl = {0469.90071}, url = {http://archive.numdam.org/articles/10.24033/msmf.261/} }
TY - CHAP AU - Hiriart-Urruty, J-B. TI - New concepts in nondifferentiable programming BT - Analyse non convexe (Pau, 1977) AU - Collectif T3 - Mémoires de la Société Mathématique de France PY - 1979 SP - 57 EP - 85 IS - 60 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/msmf.261/ DO - 10.24033/msmf.261 ID - MSMF_1979__60__57_0 ER -
%0 Book Section %A Hiriart-Urruty, J-B. %T New concepts in nondifferentiable programming %B Analyse non convexe (Pau, 1977) %A Collectif %S Mémoires de la Société Mathématique de France %D 1979 %P 57-85 %N 60 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/msmf.261/ %R 10.24033/msmf.261 %F MSMF_1979__60__57_0
Hiriart-Urruty, J-B. New concepts in nondifferentiable programming, dans Analyse non convexe (Pau, 1977), Mémoires de la Société Mathématique de France, no. 60 (1979), pp. 57-85. doi : 10.24033/msmf.261. http://archive.numdam.org/articles/10.24033/msmf.261/
[1] Optimisation: Méthodes numériques. Masson et Cie, Paris (1976). | MR | Zbl
.[2] Minimisation sans contraintes de fonctions localement Lipschitziennes : application à la programmation mi-convexe, mi-différentiable. C. R. Acad. Sc. Paris, Série A, t. 284 (1977), 959-961, and Proceedings of the 3rd Symposium on Nonlinear Programming, University of Wisconsin, Madison (to appear). | MR | Zbl
.[3] Extension of optimality conditions via supporting functions. Math. Programming 5 (1973), 267-285. | MR | Zbl
and .[4] On the cones of tangents with applications to mathematical programming. J. Optimization Theory and Appl. Vol. 13, No 4 (1974), 389-426. | MR | Zbl
, and .[5] Nonlinear programming without differentiability in Banach spaces : necessary and sufficient constraint qualification. Applicable Anal. Vol 5 (1976), 165-173. | MR | Zbl
, , and .[6] Espaces topologiques, fonctions multivoques. Dunod, Paris (1966). | Zbl
.[7] Principe de Pontryagin pour des systemes régis par une équation différentielle multivoque. Publications Mathématiques de l'université de Bordeaux I 1973-1974 (2), 25-41. | MR | Zbl
and .[8] The method of tents in the theory of extremal problems. Russian Math. Surveys 30, 3, (1975), 1-54. | MR | Zbl
.[9] Fractional programming without differentiability. Math. Programming 11 (1976), 283-290. | MR | Zbl
.[10] Espaces vectoriels topologiques. Fascicules XV, XVII, Hermann, Paris (1966-1967). | Zbl
.[11] La méthode des centres dans un espace topologique. Numer. Math. 8 (1966), 58-67. | MR | Zbl
and .[12] Necessary conditions for nonsmooth problems in optimal control and the calculus of variations. Ph. D. Dissertation, University of Washington (1973).
.[13] Generalized gradients and applications. Transactions of the American Math. Society, Vol 205 (1975), 247-262. | MR | Zbl
.[14] A new approach to Lagrange multipliers. Math. of Operations Res. 2 (1976), 165-174. | MR | Zbl
.[15] Generalized gradients of Lipschitz functionals. Madison M. R. C. Technical Summary Report, University of Wisconsin (1976).
.[16] On the inverse function theorem. Pacific J. Math., Vol 64, No 1 (1976), 97-102. | MR | Zbl
,[17] Lagrangean conditions for quasi-differentiable optimization. Research Report No 7 (1976), School of Mathematical Sciences, University of Melbourne.
and .[18] Conjugacy in quasi-convex analysis. Convex Analysis and its applications, Lecture Notes in Economics and Mathematical Systems No 144 (A. Auslender, Ed.) Springer-Verlag (1977) pp. 66-99. | MR | Zbl
.[19] Contributions à l'étude des fonctions quasi-convexes. Thèse de Doctorat ès-Sciences Mathématiques, Université de Clermont II (1977). | MR
.[20] Introduction to minimax. John Wiley and Sons, New York (1974). | MR
and .[21] On the geometrical characterization of differentiability I. Commentationes Mathematicae Universitatis Carolinae 15, 3 (1974), 521-540. | MR | Zbl
.[22] A note on geometric characterization of Fréchet-differentiability. Commentationes Mathematicae Universitatis Carolinae 17, 1 (1976), 195-204. | MR | Zbl
and .[23] Minimizing well-behaved functions. Proceedings of Twelfth Annual Allerton Conference on Circuit and System Theory. Illinois (1974), 25-34.
.[24] Lectures on mathematical theory of extremum problems. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag (1972). | MR | Zbl
.[25] Optimization of Lipschitz continuous functions. Math. Programming, Vol 13 (1977) No 1, 14-22. | MR | Zbl
.[26] Geometry of optimality conditions and constraint qualifications. Math. Programming 2 (1972), 1-18. | MR | Zbl
and .[27] Optimality conditions and constraint qualifications in Banach space. J. Optimization Theory Appl. Vol 15 (1975), No 6, 667-684. | MR | Zbl
and .[28] Quasiconjugate function and surrogate duality. Cahiers du Centre d'Etudes de Rech. Oper. Vol 15, No 4 (1973), 437-448. | MR | Zbl
and .[29] Interior mapping theorem with set-valued derivatives. Journal d'Analyse Mathématique, Vol 30 (1976), 200-207. | MR | Zbl
.[30] Optimization Theory: the finite dimensional case. J. Wiley and Sons (1975). | Zbl
.[31] Conditions nécessaires d'optimalité en programmation non différentiable. Note aux Comptes Rendus Acad. Sc. Paris t. 283, Série A (1976), 843-845. | MR | Zbl
.[32] On necessary optimality conditions in nondifferentiable programming. Math. Programming, Vol 14, (1978) (to appear). | MR | Zbl
.[33] Gradients généralisés de fonctions marginales. SIAM J. on Control and Optimization (1978) (to appear). | MR | Zbl
.[34] Contributions a la programmation mathématique: cas détérministe et stochastique. Thèse de Doctorat ès-Sciences Mathématiques, Université de Clermont II (1977). | MR
.[35] Tangent cones, generalized gradients and mathematical programming in Banach spaces. Math. of Operations Res. (1978) (to appear). | Zbl
.[36] Gradients généralisés de fonctions composées. Applications. Note aux Comptes Rendus Acad. Sc. Paris t. 285, Série A (1977), 781-784. | MR | Zbl
.[37] Sur les inégalités linéaires. Colloq. Math. 13 (1964), 107-123. | MR | Zbl
.[38] Sur la dualité et la sensibilité dans les problèmes de programme mathématique. Thèse de Doctorat ès-Sciences Mathématiques, Université de Paris VI (1974).
.[39] On the differentiability almost everywhere of functions of many variables. Vestnik Moskovskogo Universiteta, Matematika, Vol 31, No 6 (1976), 67-70 = Moscow University Mathematics Bulletin, Vol 31, No 5-6, (1976), 129-131. | Zbl
.[40] Approximation et Optimisation, Hermann (1972). | MR | Zbl
.[41] Valeur moyenne pour gradient généralisé. Note aux Comptes Rendus Acad. Sc. Paris, Série A, (1975), 795-797. | MR | Zbl
.[41] * Generic differentiability of Lipschitzian functions. Cahiers de Mathématiques de la Décision (1977), No 7704.
.[42] Sous-différentiabilité de fonctions composées. Travaux du Séminaire d'Analyse Unilatérale, Vol. 1, Exposé No 2 (1968), Université de Montpellier. | MR
.[43] On necessary and sufficient conditions for a local minimum in a problem with constraints. Soviet. Math. Dokl., Vol 14, No 3 (1973), 853-857. | Zbl
, and .[44] Nonlinear programming. Mc. Graw-Hill, New York (1972). | Zbl
.[45] Various definitions of the derivative in mathematical programming. Math. Programming 7 (1974), 144-151. | MR | Zbl
and .[46] A propos du problème des inégalités et de ses applications à la programmation et au contrôle optimal. Publications Mathématiques de l'Université de Bordeaux I, 1973-1974 (3).
.[47] Strong derivatives and inverse mappings. Amer. Math. Monthly, 81 (1974), 969-980. | MR | Zbl
.[48] The quasi-gradient method for the solving of the nonlinear programming problems. Kibernetika, 1, (1973), 122-125 = Cybernetics, Vol 9, No 1 (1974), 145-150. | Zbl
.[49] e-quasi-gradient method for solving nonsmooth extremal problems. Kibernetika, 1, (1977), 109-113 = Cybernetics, Vol 13, No 1, (1977), 109-114. | Zbl
and ,[50] Iterative solution of nonlinear equations in several valables. Acad. Press, New York and London (1970). | Zbl
and .[51] Fonctions sous-linéarisables et principe de Pontryagin. Publications Mathématiques de l'Université de Bordeaux I, 1973-1974 (3), 65-72.
.[52] Sous-différentiels de fonctions numériques non convexes. Note aux Comptes Rendus Acad. Sc. Paris, t. 278, Serie A (1974), 1553-1555. | MR | Zbl
.[53] Calcul sous-différentiel et Optimisation. Publications Mathématiques de l'Université de Pau (1974). | MR | Zbl
.[54]
(to appear).[55] Necessary conditions for an extremum. Marcel Dekker Inc., New York (1971). | MR | Zbl
.[56] Leçons sur les jeux différentiels. Cahiers de l'I.R.I.A., No 4, (1971), 145-226. | MR | Zbl
.[57] Contribution to Dubovitskii and Milyutin's optimization formalism. Optimization Techniques, Modeling and Optimization in the Service of Man. Part 2. Lecture Notes in Computer Science (J. Ceá, Ed.) Springer-Verlag (1976), 438-453. | Zbl
.[58] Convex Analysis. Princeton University Press (1970). | MR | Zbl
,[59] A class of almost-differentiable functions and a minimization method for functions of this class. Kibernetika, 8, (1972), 65-70 = Cybernetics, Vol 8, No 4, (1974), 509-606.
.[60] Singular integrals and differentiability properties of functions. Princeton Math. Ser. No 30, Princeton Univ. Press, N. J. (1970). | MR | Zbl
.[61] Propriétés des sous-différentiels des fonctions localement Lipschitzcennes définies sur un espace de Banach séparable. Applications. Thèse de Doctorat de Spécialité, Université de Montpellier (1976).
.[62] Derivate containers, Inverse functions and Controllability. Calculs of Variations and Control Theory (D. L. Russell, Ed.) Acad. Press (1976).
.[63] Conditions for an extremum of a functional in case of constraints. Cybernetics, Vol 9, No 6, (1975), 982-988.
, and .[64] Nonlinear programming: a unified approach. Prentice-Hall, Inc., N. J. (1969). | MR | Zbl
.Cité par Sources :