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

El Houcine Bergou (), Youssef Diouane () and Vyacheslav Kungurtsev ()
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El Houcine Bergou: Université Paris-Saclay
Youssef Diouane: Université de Toulouse
Vyacheslav Kungurtsev: Czech Technical University in Prague

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 13, 927-944

Abstract: 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.

Keywords: Inverse problems; Levenberg–Marquardt method; Worst-case complexity bound; Global and local convergence; 49M05; 49M15; 90C06; 90C60 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-020-01666-1

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