Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.16514 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912724026392576 |
|---|---|
| author | Nghia, Tran T. A. Vo, Nghia V. Vu, Khoa V. H. |
| author_facet | Nghia, Tran T. A. Vo, Nghia V. Vu, Khoa V. H. |
| contents | We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the tilt-stability condition at the optimal solution, these methods achieve the quadratic convergence rates expected of Newton schemes. Numerical experiments on Lasso, generalized Lasso, OSCAR-regularized least-square problems, and an image super-resolution task illustrate both the broad applicability and the accelerated convergence profile of the proposed algorithms, in comparison with first-order and several recently developed nonsmooth Newton schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonsmooth Newton methods with effective subspaces for polyhedral regularization Nghia, Tran T. A. Vo, Nghia V. Vu, Khoa V. H. Optimization and Control We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the tilt-stability condition at the optimal solution, these methods achieve the quadratic convergence rates expected of Newton schemes. Numerical experiments on Lasso, generalized Lasso, OSCAR-regularized least-square problems, and an image super-resolution task illustrate both the broad applicability and the accelerated convergence profile of the proposed algorithms, in comparison with first-order and several recently developed nonsmooth Newton schemes. |
| title | Nonsmooth Newton methods with effective subspaces for polyhedral regularization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.16514 |