{
  "abstract": "Mixed-integer programs have found applications in many real-world problems but remain difficult to solve at scale. To improve scalability, there has been increasing interest in incorporating first-order methods as subroutines for solving node relaxations, with success primarily on problems involving specific types of constraints. However, when more general constraints are considered, first-order methods cannot be directly applied because, at finite iterations, they typically produce infeasible primal and dual solutions, preventing their direct integration into branch-and-bound. To overcome this limitation, we introduce repair procedures that extract valid primal and dual bounds from infeasible first-order iterates. These bounds enable node pruning, incumbent updates, and early stopping at any iteration. Empirically, our approach achieves one to two orders of magnitude speedups when solving real-world instances (with another order of magnitude speedup when running on GPUs) and certifies optimality on instances that are difficult for commercial solvers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26509",
  "author_total": 3,
  "authors": [
    {
      "name": "Francesco Pivi"
    },
    {
      "name": "Jiachang Liu"
    },
    {
      "name": "Andrea Lodi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p812j27z2wv3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26509",
  "fulltext_url": null,
  "id": "4p812j27z2wv3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26509",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223066429",
  "pdf_url": "https://arxiv.org/pdf/2610.26509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p812j27z2wv3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "First-Order Primal-Dual Repairs for Scalable Branch and Bound",
  "title_text": "First-Order Primal-Dual Repairs for Scalable Branch and Bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4p812j27z2wv3",
  "venue": "arXiv",
  "versions": []
}