A derivative-free Levenberg-Marquardt method for sparse nonlinear least squares problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912473022464000 |
|---|---|
| author | Feng, Yuchen Wang, Chuanlong Fan, Jinyan |
| author_facet | Feng, Yuchen Wang, Chuanlong Fan, Jinyan |
| contents | This paper studies sparse nonlinear least squares problems, where the Jacobian matrices are unavailable or expensive to compute, yet have some underlying sparse structures. We construct the Jacobian models by the $ \ell_1 $ minimization subject to a small number of interpolation constraints with interpolation points generated from some certain distributions,and propose a derivative-free Levenberg-Marquardt algorithm based on such Jacobian models.It is proved that the Jacobian models are probabilistically first-order accurate and the algorithm converges globally almost surely.Numerical experiments are presented to show the efficiency of the proposed algorithm for sparse nonlinear least squares problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A derivative-free Levenberg-Marquardt method for sparse nonlinear least squares problems Feng, Yuchen Wang, Chuanlong Fan, Jinyan Optimization and Control This paper studies sparse nonlinear least squares problems, where the Jacobian matrices are unavailable or expensive to compute, yet have some underlying sparse structures. We construct the Jacobian models by the $ \ell_1 $ minimization subject to a small number of interpolation constraints with interpolation points generated from some certain distributions,and propose a derivative-free Levenberg-Marquardt algorithm based on such Jacobian models.It is proved that the Jacobian models are probabilistically first-order accurate and the algorithm converges globally almost surely.Numerical experiments are presented to show the efficiency of the proposed algorithm for sparse nonlinear least squares problems. |
| title | A derivative-free Levenberg-Marquardt method for sparse nonlinear least squares problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.06772 |