{"ID":2839147,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.16514","arxiv_id":"2511.16514","title":"Nonsmooth Newton methods with effective subspaces for polyhedral regularization","abstract":"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.","short_abstract":"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 conv...","url_abs":"https://arxiv.org/abs/2511.16514","url_pdf":"https://arxiv.org/pdf/2511.16514v2","authors":"[\"Tran T. A. Nghia\",\"Nghia V. Vo\",\"Khoa V. H. Vu\"]","published":"2025-11-20T16:32:40Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}