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

El Houcine Bergou; Youssef Diouane; Vyacheslav Kungurtsev

doi:10.1007/s10957-020-01666-1

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

El Houcine Bergou, Youssef Diouane, Vyacheslav Kungurtsev

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

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.

Original language	English (US)
Journal	Journal of Optimization Theory and Applications
DOIs	https://doi.org/10.1007/s10957-020-01666-1
State	Published - May 12 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
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”.

Access to Document

10.1007/s10957-020-01666-1

https://repository.kaust.edu.sa/bitstream/10754/662924/1/Convergence%20and%20Complexity%20Analysis%20of%20aLevenberg%e2%80%93Marquardt%20Algorithm%20for%20Inverse%20Problems.pdf

Cite this

@article{c0fceef7351e40b69d4feb2d2575ae91,

title = "Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems",

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.",

author = "Bergou, {El Houcine} and Youssef Diouane and Vyacheslav Kungurtsev",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We would like to thank Cl{\'e}ment 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”.",

year = "2020",

month = may,

day = "12",

doi = "10.1007/s10957-020-01666-1",

language = "English (US)",

journal = "Journal of Optimization Theory and Applications",

issn = "1573-2878",

publisher = "Springer New York",

}

TY - JOUR

T1 - Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems

AU - Bergou, El Houcine

AU - Diouane, Youssef

AU - Kungurtsev, Vyacheslav

N1 - KAUST Repository Item: Exported on 2020-10-01 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”.

PY - 2020/5/12

Y1 - 2020/5/12

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/662924

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

UR - http://www.scopus.com/inward/record.url?scp=85084682182&partnerID=8YFLogxK

U2 - 10.1007/s10957-020-01666-1

DO - 10.1007/s10957-020-01666-1

M3 - Article

SN - 1573-2878

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

ER -

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

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this