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M. Hanke (1997)
A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problemsInverse Problems, 13
A. Buccini, M. Donatelli, L. Reichel (2017)
Iterated Tikhonov regularization with a general penalty termNumerical Linear Algebra with Applications, 24
H. Banks, K. Murphy (1986)
Estimation of coefficients and boundary parameters in hyperbolic systemsSiam Journal on Control and Optimization, 24
D. Hutton (2010)
Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical SimulationKybernetes, 39
M. Donatelli, M. Hanke (2013)
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurringInverse Problems, 29
N. Higham (2008)
Functions of matrices - theory and computation
L. Tang (2011)
A Regularization Homotopy Iterative Method for Ill-Posed Nonlinear Least Squares Problem and its ApplicationApplied Mechanics and Materials, 90-93
B. Kaltenbacher, A. Neubauer, O. Scherzer (2008)
Iterative Regularization Methods for Nonlinear Ill-Posed Problems, 6
D. C, T. Barz, S. Körkel, G. Wozny (2015)
Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental designComput. Chem. Eng., 77
J. Nocedal, Stephen Wright (2018)
Numerical Optimization
Binder Andreas, H. Engl, Neubauer Andreas, Scherzer Otmar, C. Groetsch (1994)
Weakly closed nonlinear operators and parameter identification in parabolic equations by tikhonov regularizationApplicable Analysis, 55
A. Cornelio (2011)
Regularized nonlinear least squares methods for hit position reconstruction in small gamma camerasAppl. Math. Comput., 217
M. Hanke (1997)
Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problemsNumerical Functional Analysis and Optimization, 18
Y Wang, Y Yuan (2005)
Convergence and regularity of trust region methods for nonlinear ill-posed problemsInverse Prob., 21
A. Buccini (2017)
Regularizing preconditioners by non-stationary iterated Tikhonov with general penalty termApplied Numerical Mathematics, 116
O. Scherzer, H. Engl, K. Kunisch (1993)
Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problemsSIAM Journal on Numerical Analysis, 30
(2003)
On the regularity of trust region-cg algorithm for nonlinear ill-posed inverse problems with application to image deconvolution problem
(2018)
Levenberg–Marquardt methods for the solution of noisy nonlinear least squares problems
K. Kunisch, L. White (1987)
Parameter estimation, regularity and the penalty method for a class of two point boundary value problemsSiam Journal on Control and Optimization, 25
G. Deidda, C. Fenu, G. Rodriguez (2014)
Regularized solution of a nonlinear problem in electromagnetic soundingInverse Problems, 30
A Conn, N Gould, P Toint (2000)
Trust Region Methods
A. Rieder (1999)
On the regularization of nonlinear ill-posed problems via inexact Newton iterationsInverse Problems, 15
A. Neubauer (1988)
An a posteriori parameter choice for Tikhonov regularization in the presence of modeling errorApplied Numerical Mathematics, 4
L. Fleischer (2016)
Regularization Of Inverse Problems
S. Bellavia, B. Morini, E. Riccietti (2015)
On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementationComputational Optimization and Applications, 64
G. Landi, E. Piccolomini, J. Nagy (2017)
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesisInverse Problems, 33
J. Moré, D. Sorensen (1983)
Computing a Trust Region StepSiam Journal on Scientific and Statistical Computing, 4
(2000)
Trust Region Methods, vol
S. Henn (2003)
A Levenberg–Marquardt Scheme for Nonlinear Image RegistrationBIT Numerical Mathematics, 43
J. Dennis, Bobby Schnabel (1983)
Numerical methods for unconstrained optimization and nonlinear equations
In this paper, we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg–Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems.
Journal of Optimization Theory and Applications – Springer Journals
Published: Jun 4, 2018
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