New concepts in nondifferentiable programming
Analyse non convexe (Pau, 1977), Bulletin de la Société mathématique de France. Mémoire, no. 60 (1979), pp. 57-85 
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Hiriart-Urruty, J-B. New concepts in nondifferentiable programming, dans Analyse non convexe (Pau, 1977), Bulletin de la Société mathématique de France. Mémoire, no. 60 (1979), pp. 57-85. doi: 10.24033/msmf.261

[1] A. Auslender. Optimisation: Méthodes numériques. Masson et Cie, Paris (1976). | Zbl | MR

[2] A. Auslender. 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). | Zbl | MR

[3] M. S. Bazaraa and J. J. Goode. Extension of optimality conditions via supporting functions. Math. Programming 5 (1973), 267-285. | Zbl | MR

[4] M. S. Bazaraa, J. J. Goode and Z. Nashed. On the cones of tangents with applications to mathematical programming. J. Optimization Theory and Appl. Vol. 13, No 4 (1974), 389-426. | Zbl | MR

[5] M. S. Bazaraa, C. M. Shetty, J. J. Goode and M. Z. Nashed. Nonlinear programming without differentiability in Banach spaces : necessary and sufficient constraint qualification. Applicable Anal. Vol 5 (1976), 165-173. | Zbl | MR

[6] C. Berge. Espaces topologiques, fonctions multivoques. Dunod, Paris (1966). | Zbl

[7] H. Berliocchi and J. M. Lasry. 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. | Zbl | MR

[8] V. G. Bolt'Yanskii. The method of tents in the theory of extremal problems. Russian Math. Surveys 30, 3, (1975), 1-54. | Zbl | MR

[9] J. M. Borwein. Fractional programming without differentiability. Math. Programming 11 (1976), 283-290. | Zbl | MR

[10] N. Bourbaki. Espaces vectoriels topologiques. Fascicules XV, XVII, Hermann, Paris (1966-1967). | Zbl

[11] Buì-Trong-Liêũ and P. Huard. La méthode des centres dans un espace topologique. Numer. Math. 8 (1966), 58-67. | Zbl | MR

[12] F. H. Clarke. Necessary conditions for nonsmooth problems in optimal control and the calculus of variations. Ph. D. Dissertation, University of Washington (1973).

[13] F. H. Clarke. Generalized gradients and applications. Transactions of the American Math. Society, Vol 205 (1975), 247-262. | Zbl | MR

[14] F. H. Clarke. A new approach to Lagrange multipliers. Math. of Operations Res. 2 (1976), 165-174. | Zbl | MR

[15] F. H. Clarke. Generalized gradients of Lipschitz functionals. Madison M. R. C. Technical Summary Report, University of Wisconsin (1976).

[16] F. H. Clarke, On the inverse function theorem. Pacific J. Math., Vol 64, No 1 (1976), 97-102. | Zbl | MR

[17] B. D. Craven and B. Mond. Lagrangean conditions for quasi-differentiable optimization. Research Report No 7 (1976), School of Mathematical Sciences, University of Melbourne.

[18] J.-P. Crouzeix. 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. | Zbl | MR

[19] J.-P. Crouzeix. Contributions à l'étude des fonctions quasi-convexes. Thèse de Doctorat ès-Sciences Mathématiques, Université de Clermont II (1977). | MR

[20] V. F. Dem'Yanov and V. N. Malozemov. Introduction to minimax. John Wiley and Sons, New York (1974). | MR

[21] J. Durdil. On the geometrical characterization of differentiability I. Commentationes Mathematicae Universitatis Carolinae 15, 3 (1974), 521-540. | Zbl | MR

[22] J. Durdil and J. Daneš. A note on geometric characterization of Fréchet-differentiability. Commentationes Mathematicae Universitatis Carolinae 17, 1 (1976), 195-204. | Zbl | MR

[23] A. Feuer. Minimizing well-behaved functions. Proceedings of Twelfth Annual Allerton Conference on Circuit and System Theory. Illinois (1974), 25-34.

[24] I. V. Girsanov. Lectures on mathematical theory of extremum problems. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag (1972). | Zbl | MR

[25] A. A. Goldstein. Optimization of Lipschitz continuous functions. Math. Programming, Vol 13 (1977) No 1, 14-22. | Zbl | MR

[26] F. J. Gould and J. W. Tolle. Geometry of optimality conditions and constraint qualifications. Math. Programming 2 (1972), 1-18. | Zbl | MR

[27] F. J. Gould and J. W. Tolle. Optimality conditions and constraint qualifications in Banach space. J. Optimization Theory Appl. Vol 15 (1975), No 6, 667-684. | Zbl | MR

[28] H.J. Greenberg and W. P. Pierskalla. Quasiconjugate function and surrogate duality. Cahiers du Centre d'Etudes de Rech. Oper. Vol 15, No 4 (1973), 437-448. | Zbl | MR

[29] H. Halkin. Interior mapping theorem with set-valued derivatives. Journal d'Analyse Mathématique, Vol 30 (1976), 200-207. | Zbl | MR

[30] M. R. Hestenes. Optimization Theory: the finite dimensional case. J. Wiley and Sons (1975). | Zbl

[31] J-B. Hiriart-Urruty. Conditions nécessaires d'optimalité en programmation non différentiable. Note aux Comptes Rendus Acad. Sc. Paris t. 283, Série A (1976), 843-845. | Zbl | MR

[32] J-B. Hiriart-Urruty. On necessary optimality conditions in nondifferentiable programming. Math. Programming, Vol 14, (1978) (to appear). | Zbl | MR

[33] J-B. Hiriart-Urruty. Gradients généralisés de fonctions marginales. SIAM J. on Control and Optimization (1978) (to appear). | Zbl | MR

[34] J-B. Hiriart-Urruty. Contributions a la programmation mathématique: cas détérministe et stochastique. Thèse de Doctorat ès-Sciences Mathématiques, Université de Clermont II (1977). | MR

[35] J-B. Hiriart-Urruty. Tangent cones, generalized gradients and mathematical programming in Banach spaces. Math. of Operations Res. (1978) (to appear). | Zbl

[36] J-B. Hiriart-Urruty. Gradients généralisés de fonctions composées. Applications. Note aux Comptes Rendus Acad. Sc. Paris t. 285, Série A (1977), 781-784. | Zbl | MR

[37] Hoang Tuy. Sur les inégalités linéaires. Colloq. Math. 13 (1964), 107-123. | Zbl | MR

[38] R. Janin. Sur la dualité et la sensibilité dans les problèmes de programme mathématique. Thèse de Doctorat ès-Sciences Mathématiques, Université de Paris VI (1974).

[39] S. N. Kruzhkov. 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] P-J. Laurent. Approximation et Optimisation, Hermann (1972). | Zbl | MR

[41] G. Lebourg. Valeur moyenne pour gradient généralisé. Note aux Comptes Rendus Acad. Sc. Paris, Série A, (1975), 795-797. | Zbl | MR

[41] * G. Lebourg. Generic differentiability of Lipschitzian functions. Cahiers de Mathématiques de la Décision (1977), No 7704.

[42] C. Lescarret. Sous-différentiabilité de fonctions composées. Travaux du Séminaire d'Analyse Unilatérale, Vol. 1, Exposé No 2 (1968), Université de Montpellier. | MR

[43] E. S. Levitin, A. A. Milyutin and N. P. Osmolovskii. 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

[44] O. L. Mangasarian. Nonlinear programming. Mc. Graw-Hill, New York (1972). | Zbl

[45] H. Massam and S. Zlobec. Various definitions of the derivative in mathematical programming. Math. Programming 7 (1974), 144-151. | Zbl | MR

[46] P. Michel. 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] A. Nijenhuis. Strong derivatives and inverse mappings. Amer. Math. Monthly, 81 (1974), 969-980. | Zbl | MR

[48] E. A. Nurminskii. 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. A. Nurminskii and A. A. Zhelikhovskii, e-quasi-gradient method for solving nonsmooth extremal problems. Kibernetika, 1, (1977), 109-113 = Cybernetics, Vol 13, No 1, (1977), 109-114. | Zbl

[50] J. M. Ortega and W. C. Rheinboldt. Iterative solution of nonlinear equations in several valables. Acad. Press, New York and London (1970). | Zbl

[51] R. Pallu De La Barrière. Fonctions sous-linéarisables et principe de Pontryagin. Publications Mathématiques de l'Université de Bordeaux I, 1973-1974 (3), 65-72.

[52] J. P. Penot. Sous-différentiels de fonctions numériques non convexes. Note aux Comptes Rendus Acad. Sc. Paris, t. 278, Serie A (1974), 1553-1555. | Zbl | MR

[53] J-P. Penot. Calcul sous-différentiel et Optimisation. Publications Mathématiques de l'Université de Pau (1974). | Zbl | MR

[54] J-P. Penot (to appear).

[55] B. N. Pshenichnyi. Necessary conditions for an extremum. Marcel Dekker Inc., New York (1971). | Zbl | MR

[56] B. N. Pshenichnyi. Leçons sur les jeux différentiels. Cahiers de l'I.R.I.A., No 4, (1971), 145-226. | Zbl | MR

[57] L. Rigby. 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] R. T. Rockafellar, Convex Analysis. Princeton University Press (1970). | Zbl | MR

[59] N. Z. Shor. 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] E. M. Stein. Singular integrals and differentiability properties of functions. Princeton Math. Ser. No 30, Princeton Univ. Press, N. J. (1970). | Zbl | MR

[61] L. Thibault. 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] J. Warga. Derivate containers, Inverse functions and Controllability. Calculs of Variations and Control Theory (D. L. Russell, Ed.) Acad. Press (1976).

[63] Y. I. Zabotin, A. I. Korablev and R. F. Khabibullin. Conditions for an extremum of a functional in case of constraints. Cybernetics, Vol 9, No 6, (1975), 982-988.

[64] W. I. Zangwill. Nonlinear programming: a unified approach. Prentice-Hall, Inc., N. J. (1969). | Zbl | MR

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