Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems

Inverse Problems

Volumn 21, Issue 3, 2005, Pages 821-838

  Wang, Yanfei ^a,b   Yuan, Yaxiang ^b  

^a INSTITUTE OF REMOTE SENSING APPLICATIONS   (China)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAVIMETRIC ANALYSIS; MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; THEOREM PROVING;

NONLINEAR ILL-POSED PROBLEMS; REGULARIZATION TECHNIQUES; TRUST REGION METHODS; WELL-POSED PROBLEMS;

INVERSE PROBLEMS;

EID: 18744383616     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/3/003     Document Type: Article

References (19)

1. Bakushinsky A and Goncharsky A 1994 Ill-posed Problems: Theory and Applications (Dordrecht: Kluwer)
2. Binder A, Hanke M and Scherzer O 1996 On the Landweber iteration for nonlinear ill-posed problems J. Inverse Ill-posed Problems 4 381-9
3. Dennis J E, Gay D M and Welsch R E 1981 An adaptive nonlinear least-squares algorithm ACM Trans. Math. Softw. 7 369-83
4. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
5. Fletcher R 1987 Practical Methods of Optimisation 2nd edn (Chichester: Wiley)
6. Groetsch C W 1984 The Theory of Tikhonov Regularization for Fredholm Equations of The First Kind (Boston, MA: Pitman)
7. Hanke M, Neubauer A and Scherzer O 1995 A convergence analysis of Landweber iteration for nonlinear ill-posed problems Numer. Math. 72 21-37
8. Hanke M 1997 A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems Inverse Problems 13 79-95
9. Moré J J and Sorensen D C 1983 Computing a trust region step SIAM J. Sci. Stat. Comput. 4 553-72
10. Nocedal J and Yuan Y 1998 Combining trust region and line search techniques Advances in Nonlinear Programming ed Y Yuan (Dordrecht: Kluwer) pp 153-75
11. Scherzer O 1996 A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems Numer. Funct. Anal. Optim. 17 197-214
12. Sorensen D C 1982 Newton's method with a model trust region modification SIAM J. Numer. Anal. 19 409-26
13. Tikhonov A N and Arsenin V Y 1977 Solutions of Ill-Posed Problems (New York: Wiley)
14. Vogel C R 1990 A constrained least-squares regularization method for nonlinear ill-posed problems SIAM J. Control Optim. 28 34-49
15. Wang Y and Yuan Y 2003 A trust region method for solving distributed parameter identification problems J. Comput. Math. 21 759-72
16. Xiao T, Yu S and Wang Y 2003 Numerical Methods for Inverse Problems (Beijing: Science Press) (in Chinese)
17. Yuan Y 1994 Nonlinear programming: trust region algorithms Proc. Chinese SIAM Ann. Meeting ed S T Xiao and F Wu (Beijing: Tsinghua University Press) pp 83-97
18. Yuan Y 1998 Matrix computation problems in trust region algorithms for optimization Proc. 5th CSIAM Ann. Meeting ed Q C Zeng, T Q Li, Z S Xue and Q S Cheng (Beijing: Tsinghua University Press) pp 52-64
19. Yuan Y and Sun W 1997 Optimization Theories and Methods (Beijing: Science Press) (in Chinese)