{
  "abstract": "Branch model predictive control optimizes multiple future trajectories coupled through shared decisions, with computational demands increasing as the number of scenarios and prediction horizon grow. We present a GPU-accelerated direct linear solver for branch MPC formulations in which all trajectories share a single root decision node and evolve independently thereafter. By operating at the linear-algebra level, the solver provides a reusable backend for multiple optimization algorithms whose reduced systems have the required symmetric positive-definite structure. The solver exploits two levels of parallelism: across scenarios and along each prediction horizon. A tailored variable ordering enables horizon-parallel Cholesky factorization while preserving a single root-tail coupling block per scenario in the factor. Numerical experiments demonstrate substantial speedups over state-of-the-art sparse direct solvers, achieving factorization speedups of up to 6.0$\\times$ over cuDSS and 27.6$\\times$ over eight-thread PARDISO, with triangular solve speedups of up to 3.5$\\times$ and 15.8$\\times$, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29977",
  "author_total": 5,
  "authors": [
    {
      "name": "Fenglong Song"
    },
    {
      "name": "Luyao Zhang"
    },
    {
      "name": "Liang Wu"
    },
    {
      "name": "Ján Drgoňa"
    },
    {
      "name": "Colin N. Jones"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xw1g3kgyhgv3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29977",
  "fulltext_url": null,
  "id": "1xw1g3kgyhgv3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29977",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7214342762",
  "pdf_url": "https://arxiv.org/pdf/2609.29977",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xw1g3kgyhgv3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29977",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29977"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Accelerating Branch MPC with Two-Level Parallel Direct Solves on GPUs",
  "title_text": "Accelerating Branch MPC with Two-Level Parallel Direct Solves on GPUs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/1xw1g3kgyhgv3",
  "venue": "arXiv",
  "versions": []
}