Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems
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Convergence and Complexity Analysis of aLevenberg–Marquardt Algorithm for Inverse Problems.pdf
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2020-05-12Online Publication Date
2020-05-12Print Publication Date
2020-06Embargo End Date
2021-05-12Submitted Date
2018-09-25Permanent link to this record
http://hdl.handle.net/10754/662924
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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/s10957-020-01666-1Sponsors
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 NaturearXiv
2004.03005Additional Links
http://link.springer.com/10.1007/s10957-020-01666-1ae974a485f413a2113503eed53cd6c53
10.1007/s10957-020-01666-1