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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.16514 |
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Table of 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.