{
  "abstract": "We present cuPDQPx, a GPU-accelerated, factorization-free first-order solver for large-scale convex quadratic programming (QP). Building on the restarted reflected Halpern primal-dual framework of cuPDLPx, we introduce an auxiliary-variable splitting that yields explicit updates without linearizing the quadratic objective or solving inner quadratic subproblems. A preconditioned proximal point interpretation yields both sublinear and linear fixed-point residual convergence guarantees. For practical efficiency, cuPDQPx integrates diagonal preconditioning, step-size selection, adaptive restart, and adaptive primal and quadratic weight updates. cuPDQPx is implemented in C and CUDA with optimized sparse matrix-vector products, kernel fusion, and CUDA Graphs. Numerical experiments on the Maros-Mészáros collection, a convex subset of QPLIB, and synthetic large-scale QPs demonstrate that cuPDQPx has strong numerical performance at both $10^{-4}$ and $10^{-8}$ tolerances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38706",
  "author_total": 3,
  "authors": [
    {
      "name": "Haihao Lu"
    },
    {
      "name": "Zedong Peng"
    },
    {
      "name": "Jinwen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9my24d7k07mrp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38706",
  "fulltext_url": null,
  "id": "9my24d7k07mrp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38706",
  "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.MS"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9my24d7k07mrp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38706"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming",
  "title_text": "cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9my24d7k07mrp",
  "venue": "arXiv",
  "versions": []
}