TY - JOUR
T1 - Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems
AU - Kobayashi, Michiya
AU - Narushima, Yasushi
AU - Yabe, Hiroshi
N1 - Funding Information:
The authors would like to thank the referees for their valuable comments. The second and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 21510164 of Japan Society for the Promotion of Science.
PY - 2010/5/15
Y1 - 2010/5/15
N2 - In this paper, we deal with conjugate gradient methods for solving nonlinear least squares problems. Several Newton-like methods have been studied for solving nonlinear least squares problems, which include the Gauss-Newton method, the Levenberg-Marquardt method and the structured quasi-Newton methods. On the other hand, conjugate gradient methods are appealing for general large-scale nonlinear optimization problems. By combining the structured secant condition and the idea of Dai and Liao (2001) [20], the present paper proposes conjugate gradient methods that make use of the structure of the Hessian of the objective function of nonlinear least squares problems. The proposed methods are shown to be globally convergent under some assumptions. Finally, some numerical results are given.
AB - In this paper, we deal with conjugate gradient methods for solving nonlinear least squares problems. Several Newton-like methods have been studied for solving nonlinear least squares problems, which include the Gauss-Newton method, the Levenberg-Marquardt method and the structured quasi-Newton methods. On the other hand, conjugate gradient methods are appealing for general large-scale nonlinear optimization problems. By combining the structured secant condition and the idea of Dai and Liao (2001) [20], the present paper proposes conjugate gradient methods that make use of the structure of the Hessian of the objective function of nonlinear least squares problems. The proposed methods are shown to be globally convergent under some assumptions. Finally, some numerical results are given.
KW - Conjugate gradient method
KW - Global convergence
KW - Least squares problems
KW - Line search
KW - Structured secant condition
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U2 - 10.1016/j.cam.2009.12.031
DO - 10.1016/j.cam.2009.12.031
M3 - Article
AN - SCOPUS:77649271327
SN - 0377-0427
VL - 234
SP - 375
EP - 397
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -