{
  "abstract": "We present CLASSO, a path-following method for the LASSO subject to general linear equality and inequality constraints. The local direction is obtained from a quadratic programme on an augmented active set, which determines both the coefficients that leave zero and the weakly active inequalities that remain binding. For a positive-definite Hessian and a nonempty feasible set, this programme has a unique primal minimiser, even when the binding constraint rows are dependent, and gives the local derivative of the solution path. The construction recovers the LASSO-modified LARS direction without constraints, and over the full cone gives the segment leaving the origin. We prove that the primal path is piecewise affine with finitely many kinks, without a constraint qualification or unique multipliers. A finite path does not imply a finite traversal: re-certifying at each kink can fail to terminate. CLASSO instead follows the minimum-norm certificate along a lexicographic rate; we prove that this rule reaches $λ=0$ in exact arithmetic within an explicit bound and traverses the whole path. These results are machine-checked in Lean~4, and the floating-point implementation agrees with an exact rational one on all $210$ small test problems. We assess the implementation on a $39$-case synthetic suite and six constrained versions of the diabetes benchmark. On the $31$ nontrivial synthetic cases with $n\\ge p$, sampled relative objective differences from numerical reference solves are below $10^{-9}$ in magnitude; unnormalised endpoint differences reach $1.5\\times10^{-7}$ in magnitude. For $n<p$, matched differences range from $-3.6\\times10^{-7}$ to $2\\times10^{-9}$ across five ridge strengths. Across the synthetic and diabetes benchmarks, checks of all $580$ recorded segments found no missed interior event and all checked KKT residuals within the stated tolerances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17024",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Hobson"
    },
    {
      "name": "Luke Butcher"
    },
    {
      "name": "Lindley Lentati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3z9mfy2v6s1zf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17024",
  "fulltext_url": null,
  "id": "3z9mfy2v6s1zf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17024",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7221794341",
  "pdf_url": "https://arxiv.org/pdf/2610.17024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3z9mfy2v6s1zf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.17024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "CLASSO: a practical primal path-following algorithm for the constrained LASSO",
  "title_text": "CLASSO: a practical primal path-following algorithm for the constrained LASSO",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/3z9mfy2v6s1zf",
  "venue": "arXiv",
  "versions": []
}