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arXiv · 2406.07044

On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations

Antonio Leitão·Joel C. Rabelo·Dirk A. Lorenz·Maximilian Winkler
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Abstract

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM method.

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Antonio Leitão, Joel C. Rabelo, Dirk A. Lorenz, Maximilian Winkler. 2024-06-11. On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations. https://arxiv.org/abs/2406.07044

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