Free Access
Volume 24, Number 4, 1990
Page(s) 523 - 553
Published online 31 January 2017
  1. A. AUSLENDER (1976), Optimisation, méthodes numériques. Masson, Paris. [MR: 441204] [Zbl: 0326.90057] [Google Scholar]
  2. J. CEA (1971), Optimisation : Théories et algorithmes. Dunod. [MR: 298892] [Zbl: 0211.17402] [Google Scholar]
  3. A. R. CONN,N. GOULD & Ph. TOINT (1986), Testing a class of methods for solving minimization problems with simple bounds on the variables. Report n°86-3, University of Waterloo. [Zbl: 0645.65033] [Google Scholar]
  4. J. E. DENNIS, R. B. SCHNABEL (1983, Numerical methods for unconstrained optimization and nonlinear equations. Printice-Hall. [MR: 702023] [Zbl: 0579.65058] [Google Scholar]
  5. I. S. DUFF,J. NOCEDAL &J.K. REID (1987), The use linear programming for solutions of sparse sets of nonlinear equations. SIAM J. Sci. Stat. Comput. vol. 8, N° 2, pp. 99-108. [MR: 879405] [Zbl: 0636.65053] [Google Scholar]
  6. I. EKELAND & R. TEMAM (1974), Analyse Convexe et problèmes variationnels. Dunod, Gauthier-Villars. [MR: 463993] [Zbl: 0281.49001] [Google Scholar]
  7. R. FLETCHER (1980), Practical Methods of Optimization, vol. 1, John Wiley, New York. [MR: 585160] [Zbl: 0439.93001] [Google Scholar]
  8. F. FOGELMAN-SOULIE, P. GALLINARI, Y. LE CUN,S. THIRIA, (1987), Automata networks and artificial intelligence. In F. Fogelman-Soulie, Y. Robert, M. Tchuente (Eds.), Computing on automata networks, Manchester University Press. [MR: 942907] [Google Scholar]
  9. N. GASTINEL (1966), Analyse numérique linéaire. Hermann, Paris. [MR: 201053] [Zbl: 0151.21202] [Google Scholar]
  10. D. M. GAY (1981), Computing optimal constrained steps. SIAM J. Sci. Stat. Comput. 2, pp. 186-197. [MR: 622715] [Zbl: 0467.65027] [Google Scholar]
  11. P. E. GILL &W. MURRAY & (1972), Quasi-Newton methods for unconstrained optimization, The Journal of the Institute of Mathematics and its Applications, vol, 9, pp. 91-108. [MR: 300410] [Zbl: 0264.49026] [Google Scholar]
  12. P. E. GILL,W. MURRAY &M. H. WRIGHT (1981), Practical Optimization. Academie Press. [Zbl: 0503.90062] [MR: 634376] [Google Scholar]
  13. M. D. HEBDEN (1973), An algorithm for minimization using exact second derivatives. Atomic Energy Research Establishment report T.P. 515, Harwell, England. [Google Scholar]
  14. S. KANIEL &A. DAX (1979), A modified Newtons method for unconstrained minimization. SIAM J. Num. Anal., pp. 324-331. [MR: 526493] [Zbl: 0403.65027] [Google Scholar]
  15. P. LANCASTER (1969), Theory of Matrix. Academie Press, NewYork and London. [Zbl: 0186.05301] [MR: 245579] [Google Scholar]
  16. P. J. LAURENT (1972), Approximation et Optimisation. Hermann, Paris. [MR: 467080] [Zbl: 0238.90058] [Google Scholar]
  17. Y. LE CUN (1987), Modèles connectionnistes de l'apprentissage. Thèse de doctora, Université de Paris VI. [Google Scholar]
  18. MINOUX (1983), Programmation Mathématique. Tomel, Dunod. [Zbl: 0546.90056] [Google Scholar]
  19. M. MINSKY & S. PAPERT (1969), Perceptrons. Cambridge, MA : MIT Press. [Google Scholar]
  20. J. J. MORÉ (1978), The Levenberg-Marquart algorithm : implementation and theory. Lecture Notes in Mathematics 630, G. A. Waston, ed., Springer-Verlag, Berlin-Heidelberg-New York, pp. 105-116. [MR: 483445] [Zbl: 0372.65022] [Google Scholar]
  21. J. J. MORÉ (1983), Recent developments in algorithm and software for Trust Region Methods. Mathematical Programming, The State of the Art, Springer, Berlin, pp. 258-287. [MR: 717404] [Zbl: 0546.90077] [Google Scholar]
  22. J. J. MORÉ&D. C. SORENSEN (1979), On the use of directions of negative curvature in a modified Newton method. Math. Prog. 16, pp. 1-20. [MR: 517757] [Zbl: 0394.90093] [Google Scholar]
  23. J. J. MORÉ & D. C. SORENSEN (1981), Computing a trust region step. Argonne National Laboratory report, Argonne, Illinois. [Zbl: 0551.65042] [Google Scholar]
  24. H. MUKAI&E. POLAK (1978), A second order method for unconstrained optimization. J.O.T.A. vol. 26, pp. 501-513. [MR: 526650] [Zbl: 0373.90068] [Google Scholar]
  25. J. P. PENOT &A. ROGER, Updating the spectrum of a real matrix. Mathematics of Computation. [Google Scholar]
  26. M. J. D. POWELL (1975), Convergence properties of a class of minimization algorithms. O. L. Mangazarian, R. R. Meyer, S. M. Robinson Editors, Nonlinear prograrnming 2 pp. 1-27, Academic press, New York. [MR: 386270] [Zbl: 0321.90045] [Google Scholar]
  27. REINSCH (1967), Smoothing by spline functions. Numer. Math. 10, 177-183. [EuDML: 131782] [MR: 295532] [Zbl: 0161.36203] [Google Scholar]
  28. REINSCH (1971), Smoothing by spline functions II. Numer. Math. 16, 451-454. [EuDML: 132051] [Zbl: 1248.65020] [MR: 1553981] [Google Scholar]
  29. D. E. RHUMELHART &J. C. MCCLELLAND (1986) (Eds.), Parallel Distributed Processing. Cambridge, MA : MIT Press. [Google Scholar]
  30. F. ROBERT &S. WANG (1988), Implementation of a Neural Network on a Hypercube F.P.S. T20. Proceeding of IF1P WG 10.3 Working Conference on Parallel Processing. Pisa : Italy, 25-27 April. North-Holland. [Google Scholar]
  31. R. T. ROCKAFELLAR (1970), Convex Analysis. Princeton University Press, Princeton, New Jersey. [MR: 274683] [Zbl: 0193.18401] [Google Scholar]
  32. A. ROGER (1987), Mise à jour du spectre d'une matrice symétrique, Rapport de recherche SNEA (P), n° AR/87-970. [Google Scholar]
  33. S. ROUSSET, A. SCHREIBER &S. WANG (1988), Modélisation et simulation connexionniste de l'identification des visages en contexte. Le système FACENET RR 742 -M-. IMAG Grenoble. [Google Scholar]
  34. G. A. SHULTZ, R. B. SCHNABEL & R. H. BYRD (1985), A family of trust-regionbased algorithms for unconstrained minimization with strong global convergence properties. SIAM Journal on Numerical Analysis 22, pp. 47-67. [MR: 772882] [Zbl: 0574.65061] [Google Scholar]
  35. G. A. SHULTZ,R. B. SCHNABEL & R. H. BYRD (1988), Approximate solution of the trust region problem by minimization over two-dimensional subspaces Mathematical Programming. Vol. 40, pp. 247-263, North-Holland. [MR: 941311] [Zbl: 0652.90082] [Google Scholar]
  36. D. C. SORENSEN (1982), Newton's method with a model trust region modification. SIAM J. Numer. Anal. vol. 19, n°2, pp. 409-426. [MR: 650060] [Zbl: 0483.65039] [Google Scholar]
  37. G. W. STEWART (1973), Introduction to matrix computation. Academic Press, New York. [MR: 458818] [Zbl: 0302.65021] [Google Scholar]
  38. S. WANG (1988), Implementation of threshold automata networks with multilayers on a Hypercube F.P.S. T20. RR 725 -M-. IMAG, Grenoble. [Google Scholar]
  39. S. WANG, H. YÉ & F. ROBERT (1988), A PNML neural network for isolated words recognition. Proceedings of nEuro '88. First european conference on neural network, 6-9 Juin 1988 : Paris. [Google Scholar]
  40. Y. YUAN (1984), An example of only linear convergence of trust region algorithms for nonsmooth optimization. IMA Journal of Numerical Analysis 4, pp. 327-335. [MR: 752609] [Zbl: 0555.65037] [Google Scholar]
  41. Y. YUAN (1985), On the superlinear convergence of a trust region algorithm for nonsmooth optimization. Mathematical Programming, vol. 3, pp. 269-285. North-Holland. [MR: 783392] [Zbl: 0577.90066] [Google Scholar]

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