Lukšan, Ladislav Inexact trust region method for large sparse nonlinear least squares. (English) Zbl 0806.65060 Kybernetika 29, No. 4, 305-324 (1993). The paper presents an inexact trust region method for large sparse nonlinear least squares which uses a bidiagonalized linear least squares algorithm for direction determination. The numerical results show that this method is most efficient in comparison with other tested trust region methods for nonlinear least squares. Reviewer: F.Luban (Bucureşti) Cited in 4 Documents MSC: 65K05 Numerical mathematical programming methods 90C20 Quadratic programming Keywords:inexact trust region method; large sparse nonlinear least squares; bidiagonalized linear least squares algorithm; direction determination Software:LSQR; minpack PDF BibTeX XML Cite \textit{L. Lukšan}, Kybernetika 29, No. 4, 305--324 (1993; Zbl 0806.65060) Full Text: Link EuDML References: [1] G. Golub, W. Kahan: Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Numer. Anal. 2 (1965), 205-224. · Zbl 0194.18201 · doi:10.1137/0702016 [2] J. J. More B. S. Garbow, K. E. Hillstrom: Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981), 17-41. · Zbl 0454.65049 · doi:10.1145/355934.355936 [3] J. E. Dennis, H. H. W. Mei: An Unconstrained Optimization Algorithm which Uses Function and Gradient Vlues. Report No. TR-75-246. Dept. of Computer Sci., Cornell University 1975. [4] C. C. Paige: Bidiagonalization of matrices and solution of linear equations. SIAM J. Numer. Anal. 11 (1974), 197-209. · Zbl 0244.65023 · doi:10.1137/0711019 [5] C. C. Paige, M. A. Saunders: LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software 8 (1982), 43-71. · Zbl 0478.65016 · doi:10.1145/355984.355989 [6] M. J. D. Powell: Convergence properties of a class of minimization algoritms. Non-linear Programming 2 (O. L. Mangasarian, R. R. Meyer and S. M. Robinson, Academic Press, London 1975. [7] 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. · Zbl 0574.65061 · doi:10.1137/0722003 [8] T. Steihaug: The conjugate gradient method and trust regions in large-scale optimization. SIAM J. Numer. Anal. 20 (1983), 626-637. · Zbl 0518.65042 · doi:10.1137/0720042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.