Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems

The Levenberg–Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst-case iteration complexity rate, and a guaran...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 185; no. 3; pp. 927 - 944
Main Authors: Bergou, El Houcine, Diouane, Youssef, Kungurtsev, Vyacheslav
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2020
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Applications of Mathematics
Basic converters
Calculus of Variations and Optimal Control; Optimization
Complexity
Convergence
Engineering
General Mathematics
Inverse problems
Iterative methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Levenberg–Marquardt method
Inverse problems
Global and local convergence
Worst-case complexity bound
90C06
49M05
49M15
90C60
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:The Levenberg–Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst-case iteration complexity rate, and a guaranteed rate of local convergence for both zero and nonzero small residual problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt method that matches, simultaneously, the state of the art in all of these convergence properties with a single seamless algorithm. Numerical experiments confirm the theoretical behavior of our proposed algorithm.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01666-1