On the global complexity of a derivative-free Levenberg-Marquardt algorithm via orthogonal spherical smoothing
<|reference_start|>On the global complexity of a derivative-free Levenberg-Marquardt algorithm via orthogonal spherical smoothing: In this paper, we propose a derivative-free Levenberg-Marquardt algorithm for nonlinear least squares problems, where the Jacobian matrices are approximated via orthogonal spherical smoothing. It is shown that the gradient models which use the approximate Jacobian matrices are probabilistically first-order accurate, and the high probability complexity bound of the algorithm is also given.<|reference_end|>
@article{chen2024on,
    title={On the global complexity of a derivative-free Levenberg-Marquardt
  algorithm via orthogonal spherical smoothing},
    author={Xi Chen and Jinyan Fan},
    journal={arXiv preprint arXiv:2407.12542},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.12542},
    primaryClass={math.NA cs.NA math.OC}
}