Efficient trust region method for nonlinear least squares

Ladislav Lukšan

Kybernetika (1996)

  • Volume: 32, Issue: 2, page 105-120
  • ISSN: 0023-5954

How to cite

top

Lukšan, Ladislav. "Efficient trust region method for nonlinear least squares." Kybernetika 32.2 (1996): 105-120. <http://eudml.org/doc/27332>.

@article{Lukšan1996,
author = {Lukšan, Ladislav},
journal = {Kybernetika},
keywords = {nonlinear least squares problems; convergence; trust region method; iteration; numerical experiments},
language = {eng},
number = {2},
pages = {105-120},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Efficient trust region method for nonlinear least squares},
url = {http://eudml.org/doc/27332},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - Efficient trust region method for nonlinear least squares
JO - Kybernetika
PY - 1996
PB - Institute of Information Theory and Automation AS CR
VL - 32
IS - 2
SP - 105
EP - 120
LA - eng
KW - nonlinear least squares problems; convergence; trust region method; iteration; numerical experiments
UR - http://eudml.org/doc/27332
ER -

References

top
  1. M. Al-Baali R. Fletcher, Variational methods for nonlinear least squares, J. Optim. Theory Appl. 36 (1985), 405-421. (1985) 
  2. J. E. Dennis D. M. Gay R. E. Welsch, An adaptive nonlinear least-squares algorithm, ACM Trans. Math. Software 7 (1981), 348-368. (1981) 
  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. (1975) 
  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. (1971) 
  5. R. Fletcher C. Xu, Hybrid methods for nonlinear least squares, IMA J. Numer. Anal. 7 (1987), 371-389. (1987) Zbl0648.65051MR0968531
  6. P. E. Gill W. Murray, Newton type methods for unconstrained and linearly constrained optimization, Math. Programming 7 (1974), 311-350. (1974) MR0356503
  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. (1973) 
  8. K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2 (1944), 164-168. (1944) MR0010666
  9. L. Lukšan, Computational experience with improved variable metric methods for unconstrained minimization, Kybernetika 26 (1990), 415-431. (1990) MR1079679
  10. D. W. Marquardt, An algorithm for least squares estimation of non-linear parameters, SIAM J. Appl. Math. 11 (1963), 431-441. (1963) MR0153071
  11. J. Militký, Mathematical Models Building. VI, Mineo, Technical House, Ostrava 1989. (1989) 
  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. (1990) 
  13. J. J. Moré, The Levenberg-Marquardt algorithm. Implementation and theory, In: Numerical Analysis (G. A. Watson ed.), Springer Verlag, Berlin 1978. (1978) MR0483445
  14. J. J. Moré B. S. Garbow K. E. Hillström, Testing unconstrained optimization software, ACM Trans. Math. Software 7 (1981) 17-41. (1981) MR0607350
  15. J. J. Moré D. C. Sorensen, Computing a trust region step, SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. (1983) MR0723110
  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. (1970) Zbl0228.90043MR0272162
  17. R. B. Schnabel E. Eskow, A new Choleski factorization, SIAM J. Sci. Statist. Comput. 11 (1990), 1136-1158. (1990) MR1068501
  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. (1985) MR0772882

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.