| Title:
|
Efficient trust region method for nonlinear least squares (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
105-120 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65K05 |
| MSC:
|
90C20 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0882.65052 |
| idMR:
|
MR1385857 |
| . |
| Date available:
|
2009-09-24T19:01:14Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124177 |
| . |
| Reference:
|
[1] M. Al-Baali R. Fletcher: Variational methods for nonlinear least squares.J. Optim. Theory Appl. 36 (1985), 405-421. |
| Reference:
|
[2] J. E. Dennis D. M. Gay R. E. Welsch: An adaptive nonlinear least-squares algorithm.ACM Trans. Math. Software 7 (1981), 348-368. |
| Reference:
|
[3] J. E. Dennis H. H. W. Mei: An Unconstrained Optimization Algorithm which Uses Function and Gradient Values.Research Report No. TR-75-246. Dept. of Computer Sci., Cornell University 1975. |
| Reference:
|
[4] R. Fletcher: A Modified Marquardt Subroutine for Nonlinear Least Squares.Research Report No.R-6799, Theoretical Physics Division, A.E.R.E. Harwell 1971. |
| Reference:
|
[5] R. Fletcher C. Xu: Hybrid methods for nonlinear least squares.IMA J. Numer. Anal. 7 (1987), 371-389. Zbl 0648.65051, MR 0968531 |
| Reference:
|
[6] P. E. Gill W. Murray: Newton type methods for unconstrained and linearly constrained optimization.Math. Programming 7 (1974), 311-350. MR 0356503 |
| Reference:
|
[7] M. D. Hebden: An Algorithm for Minimization Using Exact Second Derivatives.Research Report No.TP515, Theoretical Physics Division, A.E.R.E. Harwell 1973. |
| Reference:
|
[8] K. Levenberg: A method for the solution of certain nonlinear problems in least squares.Quart. Appl. Math. 2 (1944), 164-168. MR 0010666 |
| Reference:
|
[9] L. Lukšan: Computational experience with improved variable metric methods for unconstrained minimization.Kybernetika 26 (1990), 415-431. MR 1079679 |
| Reference:
|
[10] D. W. Marquardt: An algorithm for least squares estimation of non-linear parameters.SIAM J. Appl. Math. 11 (1963), 431-441. MR 0153071 |
| Reference:
|
[11] J. Militký: Mathematical Models Building. VI.Mineo, Technical House, Ostrava 1989. |
| Reference:
|
[12] J. Militký O. Šenkýř L. Rudišar: Comparison of statistical software for nonlinear regression on IBM PC.In: COMPSTAT 90, Short communications, 1990, pp. 49-50. |
| Reference:
|
[13] J. J. Moré: The Levenberg-Marquardt algorithm. Implementation and theory.In: Numerical Analysis (G. A. Watson ed.), Springer Verlag, Berlin 1978. MR 0483445 |
| Reference:
|
[14] J. J. Moré B. S. Garbow K. E. Hillström: Testing unconstrained optimization software.ACM Trans. Math. Software 7 (1981) 17-41. MR 0607350 |
| Reference:
|
[15] J. J. Moré D. C. Sorensen: Computing a trust region step.SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. MR 0723110 |
| Reference:
|
[16] M. J. D. Powell: A new algorithm for unconstrained optimization.In: Nonlinear Programming (J. B. Rosen, O. L. Mangasarian and K. Ritter, eds.), Academic Press, London 1970. Zbl 0228.90043, MR 0272162 |
| Reference:
|
[17] R. B. Schnabel E. Eskow: A new Choleski factorization.SIAM J. Sci. Statist. Comput. 11 (1990), 1136-1158. MR 1068501 |
| Reference:
|
[18] 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 0772882 |
| . |
