{"ID":2874661,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.04264","arxiv_id":"2509.04264","title":"On computing sparse universal solvers for key problems in statistics","abstract":"We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal least-squares solvers, and simultaneous universal minimum-norm/least-squares solvers. For all of these, we present and compare several new alternative linear-optimization formulations and very effective proximal-point algorithms. Overall, we found that our new Douglas-Rachford splitting algorithms for these problems performed best.","short_abstract":"We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal least-squares solvers, and simultaneous universal minimum-norm/least-squares solvers....","url_abs":"https://arxiv.org/abs/2509.04264","url_pdf":"https://arxiv.org/pdf/2509.04264v1","authors":"[\"Ananias Sousa Machado\",\"Marcia Fampa\",\"Jon Lee\"]","published":"2025-09-04T14:42:13Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}