Training multi-layered neural network with a trust-region based algorithm
ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 4, pp. 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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {523--553},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {4},
     year = {1990},
     mrnumber = {1070968},
     zbl = {0707.90097},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1990__24_4_523_0/}
}
TY  - JOUR
AU  - Pham Dinh, T.
AU  - Wang, S.
AU  - Yassine, A.
TI  - Training multi-layered neural network with a trust-region based algorithm
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1990
SP  - 523
EP  - 553
VL  - 24
IS  - 4
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1990__24_4_523_0/
LA  - en
ID  - M2AN_1990__24_4_523_0
ER  - 
%0 Journal Article
%A Pham Dinh, T.
%A Wang, S.
%A Yassine, A.
%T Training multi-layered neural network with a trust-region based algorithm
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1990
%P 523-553
%V 24
%N 4
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1990__24_4_523_0/
%G en
%F 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: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 4, pp. 523-553. http://archive.numdam.org/item/M2AN_1990__24_4_523_0/

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

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

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

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

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 | Zbl

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

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

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

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

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

P. E. Gill & W. Murray &Amp; (1972), Quasi-Newton methods for unconstrained optimization, The Journal of the Institute of Mathematics and its Applications, vol, 9, pp. 91-108. | MR | Zbl

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

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 | Zbl

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

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

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

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

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 | Zbl

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 | Zbl

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 | Zbl

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 | Zbl

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 | Zbl

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

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

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 | Zbl

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 | Zbl

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 | Zbl

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 | Zbl

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

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 | Zbl

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 | Zbl