On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations
<|reference_start|>On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations: 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.<|reference_end|>
@article{leitão2024on,
    title={On inertial Levenberg-Marquardt type methods for solving nonlinear
  ill-posed operator equations},
    author={Antonio Leit~ao, Joel C. Rabelo, Dirk A. Lorenz, Maximilian Winkler},
    journal={arXiv preprint arXiv:2406.07044},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.07044},
    primaryClass={math.NA cs.NA}
}