{
  "abstract": "Interior-point (IP) methods are powerful second-order optimization algorithms but can make slow progress during early iterations. We propose Warm-IP, a hybrid framework that combines a path-following variant of the alternating direction method of multipliers (ADMM) with a primal--dual IP method. The ADMM phase generates a warm start that remains close to the central path, enabling the subsequent IP phase to rapidly refine the solution to high accuracy. We evaluate Warm-IP on a diverse collection of real-world and synthetic quadratic programming (QP) instances and compare it with leading commercial solvers (MOSEK and Gurobi) and open-source solvers (Clarabel, PIQP, and OSQP). We also curate and release a new benchmark of large-scale QPs from cancer radiotherapy treatment planning, built from real patient data and provided in canonical QP form, with instances containing hundreds of thousands of constraints. Warm-IP substantially outperforms existing solvers on large-scale problems. On the large-scale radiotherapy benchmark comprising 60 lung cancer cases, for example, Warm-IP solves an instance in 47 seconds on average with no failures, while the strongest competitors, MOSEK and Gurobi, average 55 seconds with failures on 23\\% of the cases and roughly 240 seconds with no failures, respectively. To support reproducibility and future benchmarking, we publicly release the implementation and benchmark data through a \\href{https://github.com/Radiotherapy-Optimization/Warm-IP}{GitHub repository}. These results demonstrate that appropriately warm-started IP methods can combine the rapid initial progress of first-order methods with the high-accuracy convergence of second-order methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13805",
  "author_total": 4,
  "authors": [
    {
      "name": "Babak Aslani"
    },
    {
      "name": "Mojtaba Tefagh"
    },
    {
      "name": "Gourav Jhanwar"
    },
    {
      "name": "Masoud Zarepisheh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6v7mm91ps67t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13805",
  "fulltext_url": null,
  "id": "b6v7mm91ps67t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13805",
  "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"
    ],
    [
      "arxiv",
      "physics.med-ph"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7221505794",
  "pdf_url": "https://arxiv.org/pdf/2610.13805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6v7mm91ps67t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.med-ph",
      "subfield": "biological-medical"
    }
  ],
  "title": "Warm-IP: A Path-Following ADMM Warm Start for Interior-Point Quadratic Programming",
  "title_text": "Warm-IP: A Path-Following ADMM Warm Start for Interior-Point Quadratic Programming",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/b6v7mm91ps67t",
  "venue": "arXiv",
  "versions": []
}