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 -