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

Bergou, El Houcine and Diouane, Youssef and Kungurtsev, Vyacheslav Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems. (2020) Journal of Optimization Theory and Applications. ISSN 0022-3239

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Official URL: https://doi.org/10.1007/s10957-020-01666-1

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.

Item Type:Article
HAL Id:hal-02639211
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université Paris-Saclay (FRANCE)
Other partners > Czech Technical University in Prague - CTU (CZECH REPUBLIC)
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Deposited On:27 May 2020 10:17

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