{
  "abstract": "We consider the Lorentz positive cone of $n\\times m$ matrices that map the Lorentz cone in $\\Rbb^m$ into the Lorentz cone in $\\Rbb^n$. The Lorentz positive cone and its dual, the cone of Lorentz separable matrices, are shown to provide polynomial-time algorithms for the problem of minimizing a bilinear objective over variables contained in ellipsoids in $\\Rbb^n$ and $\\Rbb^m$. We also demonstrate how these cones can be used to strengthen SDP relaxations of other nonconvex quadratic optimization problems, including the two-trust-region subproblem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32017",
  "author_total": 2,
  "authors": [
    {
      "name": "Samuel Burer"
    },
    {
      "name": "Kurt Anstreicher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e87sj4wq40t9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32017",
  "fulltext_url": null,
  "id": "e87sj4wq40t9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32017",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7214751177",
  "pdf_url": "https://arxiv.org/pdf/2609.32017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e87sj4wq40t9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Applications of the Lorentz positive cone in nonconvex quadratic optimization",
  "title_text": "Applications of the Lorentz positive cone in nonconvex quadratic optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/e87sj4wq40t9p",
  "venue": "arXiv",
  "versions": []
}