The convergence analysis of inexact Gauss-Newton methods for nonlinear problems

被引：19

作者：

Chen, Jinhai ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2008年 / 40卷 / 01期

关键词：

nonlinear least squares problems; inexact Gauss-Newton methods; weak Lipschitz condition; convergence ball;

D O I：

10.1007/s10589-007-9071-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, inexact Gauss-Newton methods for nonlinear least squares problems are studied. Under the hypothesis that derivative satisfies some kinds of weak Lipschitz conditions, the local convergence properties of inexact Gauss-Newton and inexact Gauss-Newton like methods for nonlinear problems are established with the modified relative residual control. The obtained results can provide an estimate of convergence ball for inexact Gauss-Newton methods.

引用

页码：97 / 118

页数：22

共 22 条

[1] Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Chen, JH
Li, WG
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 191 (01) : 143 - 164
[2] Convergence of Gauss-Newton's method and uniqueness of the solution
Chen, JH
Li, WG
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2005, 170 (01) : 686 - 705
[3] INEXACT NEWTON METHODS
DEMBO, RS
EISENSTAT, SC
STEIHAUG, T
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (02) : 400 - 408
[4] Dennis, 1996, NUMERICAL METHODS UN
[5] AFFINE INVARIANT CONVERGENCE THEOREMS FOR NEWTONS METHOD AND EXTENSIONS TO RELATED METHODS
DEUFLHARD, P
HEINDL, G
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (01) : 1 - 10
[6] The numerical solution of large systems of stiff IVPs for ODEs
Jackson, KR
[J]. APPLIED NUMERICAL MATHEMATICS, 1996, 20 (1-2) : 5 - 20
[7] Kantorovich LV, 1982, Functional Analysis
[8] Kelley C., 1995, FRONTIERS APPL MATH, V16
[9] Li C, 2004, COMPUT MATH APPL, V47, P1057, DOI [10.1016/S0898-1221(04)90086-7, 10.1016/j.camwa.2002.12.014]
[10] INEXACT NEWTON METHODS FOR SOLVING NONSMOOTH EQUATIONS
MARTINEZ, JM
QI, LQ
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1995, 60 (1-2) : 127 - 145

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