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

dc.contributor.authorBergou, El Houcine
dc.contributor.authorDiouane, Youssef
dc.contributor.authorKungurtsev, Vyacheslav
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionMaIAGE, INRAE, Université Paris-Saclay, 78350, Jouy-en-Josas, France
dc.contributor.institutionISAE-SUPAERO, Université de Toulouse, 31055, Toulouse Cedex 4, France
dc.contributor.institutionDepartment of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic
dc.date.accepted2020-04-06
dc.date.accessioned2020-05-31T08:08:48Z
dc.date.available2020-05-31T08:08:48Z
dc.date.issued2020-05-12
dc.date.published-online2020-05-12
dc.date.published-print2020-06
dc.date.submitted2018-09-25
dc.description.abstractThe 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.
dc.description.sponsorshipWe 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”.
dc.eprint.versionPost-print
dc.identifier.arxivid2004.03005
dc.identifier.citationBergou, 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
dc.identifier.doi10.1007/s10957-020-01666-1
dc.identifier.eid2-s2.0-85084682182
dc.identifier.issn1573-2878
dc.identifier.issn0022-3239
dc.identifier.journalJournal of Optimization Theory and Applications
dc.identifier.urihttp://hdl.handle.net/10754/662924
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/10.1007/s10957-020-01666-1
dc.rightsArchived with thanks to Journal of Optimization Theory and Applications
dc.rights.embargodate2021-05-12
dc.titleConvergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems
dc.typeArticle
display.details.left<span><h5>Embargo End Date</h5>2021-05-12<br><br><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Bergou, El Houcine,equals">Bergou, El Houcine</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-6609-7330&spc.sf=dc.date.issued&spc.sd=DESC">Diouane, Youssef</a> <a href="https://orcid.org/0000-0002-6609-7330" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Kungurtsev, Vyacheslav,equals">Kungurtsev, Vyacheslav</a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><br><h5>Online Publication Date</h5>2020-05-12<br><br><h5>Print Publication Date</h5>2020-06<br><br><h5>Date</h5>2020-05-12<br><br><h5>Submitted Date</h5>2018-09-25</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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<br><br><h5>Acknowledgements</h5>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”.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Springer Nature,equals">Springer Nature</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Journal of Optimization Theory and Applications,equals">Journal of Optimization Theory and Applications</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1007/s10957-020-01666-1">10.1007/s10957-020-01666-1</a><br><br><h5>arXiv</h5><a href="https://arxiv.org/abs/2004.03005">2004.03005</a><br><br><h5>Additional Links</h5>http://link.springer.com/10.1007/s10957-020-01666-1</span>
kaust.personBergou, El Houcine
orcid.id0000-0002-6609-7330
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