On the convergence of an inexact Gauss–Newton trust-region method for nonlinear least-squares problems with simple bounds

We introduce an inexact Gauss–Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to sol...

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Bibliographic Details
Published inOptimization letters Vol. 7; no. 3; pp. 447 - 465
Main Author Porcelli, Margherita
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2013
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Bound-constrained nonlinear least-squares
Affine scaling
Convergence theory
Trust-region methods
Simple bounds
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ISSN1862-4472
1862-4480
DOI10.1007/s11590-011-0430-z

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Summary:We introduce an inexact Gauss–Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. Some numerical illustration is also presented.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-011-0430-z