Geodesic
Combined trust region methods for nonlinear least squares
Kybernetika, Tome 32 (1996) no. 2, pp. 121-138

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR   Zbl

Classification : 65K05, 90C20, 90C30 
Lukšan, Ladislav. Combined trust region methods for nonlinear least squares. Kybernetika, Tome 32 (1996) no. 2, pp. 121-138. http://geodesic.mathdoc.fr/item/KYB_1996_32_2_a1/
@article{KYB_1996_32_2_a1,
     author = {Luk\v{s}an, Ladislav},
     title = {Combined trust region methods for nonlinear least squares},
     journal = {Kybernetika},
     pages = {121--138},
     year = {1996},
     volume = {32},
     number = {2},
     mrnumber = {1385858},
     zbl = {0882.65053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1996_32_2_a1/}
}
TY  - JOUR
AU  - Lukšan, Ladislav
TI  - Combined trust region methods for nonlinear least squares
JO  - Kybernetika
PY  - 1996
SP  - 121
EP  - 138
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_1996_32_2_a1/
LA  - en
ID  - KYB_1996_32_2_a1
ER  - 
%0 Journal Article
%A Lukšan, Ladislav
%T Combined trust region methods for nonlinear least squares
%J Kybernetika
%D 1996
%P 121-138
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_1996_32_2_a1/
%G en
%F KYB_1996_32_2_a1

[1] M. Al-Baali R. Fletcher: Variational methods for nonlinear least squares. J. Optim. Theory Appl. 36 (1985), 405-421.

[2] R. H. Byrd R. B. Schnabel G. A. Shultz: Approximate solution of the trust region problem by minimization over two-dimensional subspaces. Math. Programming 40 (1988), 247-263. | MR

[3] J. E. Dennis: Some computational techniques for the nonlinear least squares problem. In: Numerical solution of nonlinear algebraic equations (G. D. Byrne, C. A. Hall, eds.), Academic Press, London 1974.

[4] J. E. Dennis H. H. W. Mei: An Unconstrained Optimization Algorithm which Uses Function and Gradient Values. Research Report No. TR-75-246, Department of Computer Science, Cornell University 1975.

[5] J. E. Dennis D. M. Gay R. E. Welsch: An adaptive nonlinear least-squares algorithm. ACM Trans. Math. Software 7 (1981), 348-368.

[6] J. E. Dennis R. B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, New Jersey 1983. | MR

[7] R. Fletcher: A Modified Marquardt Subroutine for Nonlinear Least Squares. Research Report No.R-6799, Theoretical Physics Division, A.E.R.E. Harwell 1971.

[8] R. Fletcher: Practical Methods of Optimization. J. Wiley \& Sons, Chichester 1987. | MR | Zbl

[9] R. Fletcher C. Xu: Hybrid methods for nonlinear least squares. IMA J. Numer. Anal. 7 (1987), 371-389. | MR | Zbl

[10] P. E. Gill W. Murray: Newton type methods for unconstrained and linearly constrained optimization. Math. Programming 7 (1974), 311-350. | MR

[11] G. H. Golub C. F. Van Loan: Matrix Computations. Johns Hopkins University Press, Baltimore 1989. | MR

[12] M. R. Hestenes: Conjugate Direction Methods in Optimization. Springer-Verlag, Berlin 1980. | MR | Zbl

[13] K. Levenberg: A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2 (1944), 164-168. | MR

[14] L. Lukšan: Inexact trust region method for large sparse nonlinear least squares. Kybernetika 29 (1993), 305-324. | MR

[15] L. Lukšan: Hybrid methods for large sparse nonlinear least squares. J. Optim. Theory Appl. 89 (1996), to appear. | MR

[16] D. W. Marquardt: An algorithm for least squares estimation of non-linear parameters. SIAM J. Appl. Math. 11 (1963), 431-441. | MR

[17] J. J. Moré B. S. Garbow K. E. Hillström: Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981), 17-41. | MR

[18] J. J. Moré D. C. Sorensen: Computing a trust region step. SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. | MR

[19] M. J. D. Powell: A new algorithm for unconstrained optimization. In: Nonlinear Programming (J. B. Rosen, O. L. Mangasarian, K. Ritter, eds.), Academic Press, London 1970. | MR | Zbl

[20] M. J. D. Powell: On the global convergence of trust region algorithms for unconstrained minimization. Math. Programming 29 (1984), 297-303. | MR | Zbl

[21] G. A. Shultz R. B. Schnabel R. H. Byrd: A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties. SIAM J. Numer. Anal. 22 (1985), 47-67. | MR

[22] T. Steihaug: The conjugate gradient method and trust regions in large-scale optimization. SIAM J. Numer. Anal. 20 (1983), 626-637. | MR | Zbl