Combined trust region methods for nonlinear least squares

Ladislav Lukšan

Kybernetika (1996)

  • Volume: 32, Issue: 2, page 121-138
  • ISSN: 0023-5954

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Lukšan, Ladislav. "Combined trust region methods for nonlinear least squares." Kybernetika 32.2 (1996): 121-138. <http://eudml.org/doc/27336>.

@article{Lukšan1996,
author = {Lukšan, Ladislav},
journal = {Kybernetika},
keywords = {trust region method; Gauss-Newton method; nonlinear least squares problems; algorithms; multiple dog-leg strategy; conjugate gradient Lanczos strategies; numerical experiments},
language = {eng},
number = {2},
pages = {121-138},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Combined trust region methods for nonlinear least squares},
url = {http://eudml.org/doc/27336},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - Combined trust region methods for nonlinear least squares
JO - Kybernetika
PY - 1996
PB - Institute of Information Theory and Automation AS CR
VL - 32
IS - 2
SP - 121
EP - 138
LA - eng
KW - trust region method; Gauss-Newton method; nonlinear least squares problems; algorithms; multiple dog-leg strategy; conjugate gradient Lanczos strategies; numerical experiments
UR - http://eudml.org/doc/27336
ER -

References

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  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. (1988) MR0941311
  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. (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. (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. (1981) 
  6. J. E. Dennis R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey 1983. (1983) MR0702023
  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. (1971) 
  8. R. Fletcher, Practical Methods of Optimization, J. Wiley & Sons, Chichester 1987. (1987) Zbl0905.65002MR0955799
  9. R. Fletcher C. Xu, Hybrid methods for nonlinear least squares, IMA J. Numer. Anal. 7 (1987), 371-389. (1987) Zbl0648.65051MR0968531
  10. P. E. Gill W. Murray, Newton type methods for unconstrained and linearly constrained optimization, Math. Programming 7 (1974), 311-350. (1974) MR0356503
  11. G. H. Golub C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore 1989. (1989) MR1002570
  12. M. R. Hestenes, Conjugate Direction Methods in Optimization, Springer-Verlag, Berlin 1980. (1980) Zbl0439.49001MR0561510
  13. K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2 (1944), 164-168. (1944) MR0010666
  14. L. Lukšan, Inexact trust region method for large sparse nonlinear least squares, Kybernetika 29 (1993), 305-324. (1993) MR1247880
  15. L. Lukšan, Hybrid methods for large sparse nonlinear least squares, J. Optim. Theory Appl. 89 (1996), to appear. (1996) MR1393364
  16. D. W. Marquardt, An algorithm for least squares estimation of non-linear parameters, SIAM J. Appl. Math. 11 (1963), 431-441. (1963) MR0153071
  17. J. J. Moré B. S. Garbow K. E. Hillström, Testing unconstrained optimization software, ACM Trans. Math. Software 7 (1981), 17-41. (1981) MR0607350
  18. J. J. Moré D. C. Sorensen, Computing a trust region step, SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. (1983) MR0723110
  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. (1970) Zbl0228.90043MR0272162
  20. M. J. D. Powell, On the global convergence of trust region algorithms for unconstrained minimization, Math. Programming 29 (1984), 297-303. (1984) Zbl0569.90069MR0753758
  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. (1985) MR0772882
  22. T. Steihaug, The conjugate gradient method and trust regions in large-scale optimization, SIAM J. Numer. Anal. 20 (1983), 626-637. (1983) Zbl0518.65042MR0701102

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