| Title:
|
Combined trust region methods for nonlinear least squares (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
121-138 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65K05 |
| MSC:
|
90C20 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0882.65053 |
| idMR:
|
MR1385858 |
| . |
| Date available:
|
2009-09-24T19:01:21Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124181 |
| . |
| Reference:
|
[1] M. Al-Baali R. Fletcher: Variational methods for nonlinear least squares.J. Optim. Theory Appl. 36 (1985), 405-421. |
| Reference:
|
[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 0941311 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[5] J. E. Dennis D. M. Gay R. E. Welsch: An adaptive nonlinear least-squares algorithm.ACM Trans. Math. Software 7 (1981), 348-368. |
| Reference:
|
[6] J. E. Dennis R. B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations.Prentice-Hall, Englewood Cliffs, New Jersey 1983. MR 0702023 |
| Reference:
|
[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. |
| Reference:
|
[8] R. Fletcher: Practical Methods of Optimization.J. Wiley \& Sons, Chichester 1987. Zbl 0905.65002, MR 0955799 |
| Reference:
|
[9] R. Fletcher C. Xu: Hybrid methods for nonlinear least squares.IMA J. Numer. Anal. 7 (1987), 371-389. Zbl 0648.65051, MR 0968531 |
| Reference:
|
[10] P. E. Gill W. Murray: Newton type methods for unconstrained and linearly constrained optimization.Math. Programming 7 (1974), 311-350. MR 0356503 |
| Reference:
|
[11] G. H. Golub C. F. Van Loan: Matrix Computations.Johns Hopkins University Press, Baltimore 1989. MR 1002570 |
| Reference:
|
[12] M. R. Hestenes: Conjugate Direction Methods in Optimization.Springer-Verlag, Berlin 1980. Zbl 0439.49001, MR 0561510 |
| Reference:
|
[13] K. Levenberg: A method for the solution of certain nonlinear problems in least squares.Quart. Appl. Math. 2 (1944), 164-168. MR 0010666 |
| Reference:
|
[14] L. Lukšan: Inexact trust region method for large sparse nonlinear least squares.Kybernetika 29 (1993), 305-324. MR 1247880 |
| Reference:
|
[15] L. Lukšan: Hybrid methods for large sparse nonlinear least squares.J. Optim. Theory Appl. 89 (1996), to appear. MR 1393364 |
| Reference:
|
[16] D. W. Marquardt: An algorithm for least squares estimation of non-linear parameters.SIAM J. Appl. Math. 11 (1963), 431-441. MR 0153071 |
| Reference:
|
[17] J. J. Moré B. S. Garbow K. E. Hillström: Testing unconstrained optimization software.ACM Trans. Math. Software 7 (1981), 17-41. MR 0607350 |
| Reference:
|
[18] J. J. Moré D. C. Sorensen: Computing a trust region step.SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. MR 0723110 |
| Reference:
|
[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. Zbl 0228.90043, MR 0272162 |
| Reference:
|
[20] M. J. D. Powell: On the global convergence of trust region algorithms for unconstrained minimization.Math. Programming 29 (1984), 297-303. Zbl 0569.90069, MR 0753758 |
| Reference:
|
[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 0772882 |
| Reference:
|
[22] T. Steihaug: The conjugate gradient method and trust regions in large-scale optimization.SIAM J. Numer. Anal. 20 (1983), 626-637. Zbl 0518.65042, MR 0701102 |
| . |
