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

UR - http://www.scopus.com/inward/record.url?scp=77649271327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77649271327&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2009.12.031

DO - 10.1016/j.cam.2009.12.031

M3 - Article

AN - SCOPUS:77649271327

VL - 234

SP - 375

EP - 397

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -