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    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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    Description:
    Accepted manuscript
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    Type
    Article
    Authors
    Bergou, El Houcine
    Diouane, Youssef cc
    Kungurtsev, Vyacheslav
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-05-12
    Online Publication Date
    2020-05-12
    Print Publication Date
    2020-06
    Embargo End Date
    2021-05-12
    Submitted Date
    2018-09-25
    Permanent link to this record
    http://hdl.handle.net/10754/662924
    
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    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
    Sponsors
    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
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10957-020-01666-1
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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