An Enhanced Levenberg-Marquardt Method via Gram Reduction
Abstract
This paper studies the problem of solving the system of nonlinear equations. We propose the Gram-reduced Levenberg--Marquardt method, which reuses the Gram matrix. Our method has a global convergence guarantee without relying on any step of line-search or solving sub-problems. We show that our method takes a smaller computational complexity than existing Levenberg--Marquardt methods to find the stationary point of the square norm of the equations. We also show that the proposed method enjoys a local superlinear convergence rate under the non-degenerate assumption. Experiments are conducted on real-world applications in scientific computing and machine learning, which validate the efficiency of our method.
Cite
Text
Liu et al. "An Enhanced Levenberg-Marquardt Method via Gram Reduction." AAAI Conference on Artificial Intelligence, 2025. doi:10.1609/AAAI.V39I18.34066Markdown
[Liu et al. "An Enhanced Levenberg-Marquardt Method via Gram Reduction." AAAI Conference on Artificial Intelligence, 2025.](https://mlanthology.org/aaai/2025/liu2025aaai-enhanced/) doi:10.1609/AAAI.V39I18.34066BibTeX
@inproceedings{liu2025aaai-enhanced,
title = {{An Enhanced Levenberg-Marquardt Method via Gram Reduction}},
author = {Liu, Chengchang and Luo, Luo and Lui, John C. S.},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2025},
pages = {18772-18779},
doi = {10.1609/AAAI.V39I18.34066},
url = {https://mlanthology.org/aaai/2025/liu2025aaai-enhanced/}
}