{"paper":{"title":"The Homotopy Method Revisited: Computing Solution Paths of $\\ell_1$-Regularized Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bj\\\"orn Bringmann, Daniel Cremers, Felix Krahmer, Michael M\\\"oller","submitted_at":"2016-04-30T07:47:29Z","abstract_excerpt":"$ \\ell_1 $-regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter $ t \\in \\mathbb{R}_{\\geq 0} $ is a delicate issue. Instead of solving the variational problem for a fixed parameter, the idea of the homotopy method is to compute a complete solution path $ u(t) $ as a function of $ t $. In a celebrated paper by Osborne, Presnell, and Turlach, it has been shown that the computational cost of this approach is often comparable to the cost of solving the corresponding least squares problem. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00071","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}