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Article Dans Une Revue Journal of Optimization Theory and Applications Année : 2020

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

Résumé

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.
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Dates et versions

hal-02639211 , version 1 (28-05-2020)

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El Houcine Bergou, Youssef Diouane, Vyacheslav Kungurtsev. Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems. Journal of Optimization Theory and Applications, 2020, 185 (3), pp.927-944. ⟨10.1007/s10957-020-01666-1⟩. ⟨hal-02639211⟩
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