@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}, volume = {24}, year = {1990}, pages = {523-553}, mrnumber = {1070968}, zbl = {0707.90097}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 24 (1990) pp. 523-553. http://gdmltest.u-ga.fr/item/M2AN_1990__24_4_523_0/
Optimisation, méthodes numériques. Masson, Paris. | MR 441204 | Zbl 0326.90057
(1976),Optimisation : Théories et algorithmes. Dunod. | MR 298892 | Zbl 0211.17402
(1971),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
, & (1986),Numerical methods for unconstrained optimization and nonlinear equations. Printice-Hall. | MR 702023 | Zbl 0579.65058
, (1983,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
, & (1987),Analyse Convexe et problèmes variationnels. Dunod, Gauthier-Villars. | MR 463993 | Zbl 0281.49001
& (1974),Practical Methods of Optimization, vol. 1, John Wiley, New York. | MR 585160 | Zbl 0439.93001
(1980),Automata networks and artificial intelligence. In F. Fogelman-Soulie, Y. Robert, M. Tchuente (Eds.), Computing on automata networks, Manchester University Press. | MR 942907
, , , , (1987),Analyse numérique linéaire. Hermann, Paris. | MR 201053 | Zbl 0151.21202
(1966),Computing optimal constrained steps. SIAM J. Sci. Stat. Comput. 2, pp. 186-197. | MR 622715 | Zbl 0467.65027
(1981),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
& (1972),Practical Optimization. Academie Press. | MR 634376
, & (1981),An algorithm for minimization using exact second derivatives. Atomic Energy Research Establishment report T.P. 515, Harwell, England.
(1973),A modified Newtons method for unconstrained minimization. SIAM J. Num. Anal., pp. 324-331. | MR 526493 | Zbl 0403.65027
& (1979),Theory of Matrix. Academie Press, NewYork and London. | MR 245579
(1969),Approximation et Optimisation. Hermann, Paris. | MR 467080 | Zbl 0238.90058
(1972),Modèles connectionnistes de l'apprentissage. Thèse de doctora, Université de Paris VI.
(1987),Programmation Mathématique. Tomel, Dunod. | Zbl 0546.90056
(1983),Perceptrons. Cambridge, MA : MIT Press.
& (1969),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
(1978),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
(1983),On the use of directions of negative curvature in a modified Newton method. Math. Prog. 16, pp. 1-20. | MR 517757 | Zbl 0394.90093
& (1979),Computing a trust region step. Argonne National Laboratory report, Argonne, Illinois.
& (1981),A second order method for unconstrained optimization. J.O.T.A. vol. 26, pp. 501-513. | MR 526650 | Zbl 0373.90068
& (1978),Updating the spectrum of a real matrix. Mathematics of Computation.
& ,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
(1975),Smoothing by spline functions. Numer. Math. 10, 177-183. | MR 295532 | Zbl 0161.36203
(1967),Smoothing by spline functions II. Numer. Math. 16, 451-454. | MR 1553981
(1971),Parallel Distributed Processing. Cambridge, MA : MIT Press.
& (1986) (Eds.),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.
& (1988),Convex Analysis. Princeton University Press, Princeton, New Jersey. | MR 274683 | Zbl 0193.18401
(1970),Mise à jour du spectre d'une matrice symétrique, Rapport de recherche SNEA (P), n° AR/87-970.
(1987),Modélisation et simulation connexionniste de l'identification des visages en contexte. Le système FACENET RR 742 -M-. IMAG Grenoble.
, & (1988),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
, & (1985),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
, & (1988),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
(1982),Introduction to matrix computation. Academic Press, New York. | MR 458818 | Zbl 0302.65021
(1973),Implementation of threshold automata networks with multilayers on a Hypercube F.P.S. T20. RR 725 -M-. IMAG, Grenoble.
(1988),A PNML neural network for isolated words recognition. Proceedings of nEuro '88. First european conference on neural network, 6-9 Juin 1988 : Paris.
, & (1988),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
(1984),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
(1985),