Previous |  Up |  Next


[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 0941311
[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 0702023
[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 0955799 | Zbl 0905.65002
[9] R. Fletcher C. Xu: Hybrid methods for nonlinear least squares. IMA J. Numer. Anal. 7 (1987), 371-389. MR 0968531 | Zbl 0648.65051
[10] P. E. Gill W. Murray: Newton type methods for unconstrained and linearly constrained optimization. Math. Programming 7 (1974), 311-350. MR 0356503
[11] G. H. Golub C. F. Van Loan: Matrix Computations. Johns Hopkins University Press, Baltimore 1989. MR 1002570
[12] M. R. Hestenes: Conjugate Direction Methods in Optimization. Springer-Verlag, Berlin 1980. MR 0561510 | Zbl 0439.49001
[13] K. Levenberg: A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2 (1944), 164-168. MR 0010666
[14] L. Lukšan: Inexact trust region method for large sparse nonlinear least squares. Kybernetika 29 (1993), 305-324. MR 1247880
[15] L. Lukšan: Hybrid methods for large sparse nonlinear least squares. J. Optim. Theory Appl. 89 (1996), to appear. MR 1393364
[16] D. W. Marquardt: An algorithm for least squares estimation of non-linear parameters. SIAM J. Appl. Math. 11 (1963), 431-441. MR 0153071
[17] J. J. Moré B. S. Garbow K. E. Hillström: Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981), 17-41. MR 0607350
[18] J. J. Moré D. C. Sorensen: Computing a trust region step. SIAM J. Sci. Statist. Comput. 4 (1983), 553-572. MR 0723110
[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 0272162 | Zbl 0228.90043
[20] M. J. D. Powell: On the global convergence of trust region algorithms for unconstrained minimization. Math. Programming 29 (1984), 297-303. MR 0753758 | Zbl 0569.90069
[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
[22] T. Steihaug: The conjugate gradient method and trust regions in large-scale optimization. SIAM J. Numer. Anal. 20 (1983), 626-637. MR 0701102 | Zbl 0518.65042
Partner of
EuDML logo