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

Embargo End Date
2021-05-12

Type
Article

Authors
Bergou, El Houcine
Diouane, Youssef
Kungurtsev, Vyacheslav

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2020-05-12

Print Publication Date
2020-06

Date
2020-05-12

Submitted Date
2018-09-25

Abstract
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.

Citation
Bergou, E. H., Diouane, Y., & Kungurtsev, V. (2020). Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems. Journal of Optimization Theory and Applications. doi:10.1007/s10957-020-01666-1

Acknowledgements
We would like to thank Clément Royer and the referees for their careful readings and corrections that helped us to improve our manuscript significantly. Support for Vyacheslav Kungurtsev was provided by the OP VVV Project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”.

Publisher
Springer Nature

Journal
Journal of Optimization Theory and Applications

DOI
10.1007/s10957-020-01666-1

arXiv
2004.03005

Additional Links
http://link.springer.com/10.1007/s10957-020-01666-1

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