Training multi-layered neural network with a trust-region based algorithm
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 24 (1990) no. 4, p. 523-553
@article{M2AN_1990__24_4_523_0,
     author = {Pham Dinh, T. and Wang, S. and Yassine, A.},
     title = {Training multi-layered neural network with a trust-region based algorithm},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {24},
     number = {4},
     year = {1990},
     pages = {523-553},
     zbl = {0707.90097},
     mrnumber = {1070968},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1990__24_4_523_0}
}
Pham Dinh, T.; Wang, S.; Yassine, A. Training multi-layered neural network with a trust-region based algorithm. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 24 (1990) no. 4, pp. 523-553. http://www.numdam.org/item/M2AN_1990__24_4_523_0/

A. Auslender (1976), Optimisation, méthodes numériques. Masson, Paris. | MR 441204 | Zbl 0326.90057

J. Cea (1971), Optimisation : Théories et algorithmes. Dunod. | MR 298892 | Zbl 0211.17402

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

J. E. Dennis, R. B. Schnabel (1983, Numerical methods for unconstrained optimization and nonlinear equations. Printice-Hall. | MR 702023 | Zbl 0579.65058

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

I. Ekeland & R. Temam (1974), Analyse Convexe et problèmes variationnels. Dunod, Gauthier-Villars. | MR 463993 | Zbl 0281.49001

R. Fletcher (1980), Practical Methods of Optimization, vol. 1, John Wiley, New York. | MR 585160 | Zbl 0439.93001

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

N. Gastinel (1966), Analyse numérique linéaire. Hermann, Paris. | MR 201053 | Zbl 0151.21202

D. M. Gay (1981), Computing optimal constrained steps. SIAM J. Sci. Stat. Comput. 2, pp. 186-197. | MR 622715 | Zbl 0467.65027

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

P. E. Gill, W. Murray &M. H. Wright (1981), Practical Optimization. Academie Press. | MR 634376

M. D. Hebden (1973), An algorithm for minimization using exact second derivatives. Atomic Energy Research Establishment report T.P. 515, Harwell, England.

S. Kaniel & A. Dax (1979), A modified Newtons method for unconstrained minimization. SIAM J. Num. Anal., pp. 324-331. | MR 526493 | Zbl 0403.65027

P. Lancaster (1969), Theory of Matrix. Academie Press, NewYork and London. | MR 245579

P. J. Laurent (1972), Approximation et Optimisation. Hermann, Paris. | MR 467080 | Zbl 0238.90058

Y. Le Cun (1987), Modèles connectionnistes de l'apprentissage. Thèse de doctora, Université de Paris VI.

Minoux (1983), Programmation Mathématique. Tomel, Dunod. | Zbl 0546.90056

M. Minsky & S. Papert (1969), Perceptrons. Cambridge, MA : MIT Press.

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

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

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

J. J. Moré & D. C. Sorensen (1981), Computing a trust region step. Argonne National Laboratory report, Argonne, Illinois.

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

J. P. Penot &A. Roger, Updating the spectrum of a real matrix. Mathematics of Computation.

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

Reinsch (1967), Smoothing by spline functions. Numer. Math. 10, 177-183. | MR 295532 | Zbl 0161.36203

Reinsch (1971), Smoothing by spline functions II. Numer. Math. 16, 451-454. | MR 1553981

D. E. Rhumelhart &J. C. Mcclelland (1986) (Eds.), Parallel Distributed Processing. Cambridge, MA : MIT Press.

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.

R. T. Rockafellar (1970), Convex Analysis. Princeton University Press, Princeton, New Jersey. | MR 274683 | Zbl 0193.18401

A. Roger (1987), Mise à jour du spectre d'une matrice symétrique, Rapport de recherche SNEA (P), n° AR/87-970.

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.

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

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

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

G. W. Stewart (1973), Introduction to matrix computation. Academic Press, New York. | MR 458818 | Zbl 0302.65021

S. Wang (1988), Implementation of threshold automata networks with multilayers on a Hypercube F.P.S. T20. RR 725 -M-. IMAG, Grenoble.

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.

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

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