{
  "abstract": "Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization. We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape. We warm-start PPR with Combinatorial Multigrid (CMG), a spectral graph-coarsening method that produces structure-aware initial solutions in near-linear time without training data. On \\texttt{t2g20} ($n=400$), benchmark instance with known exact optimum, the combined CMG+PPR pipeline reaches $97.5\\%$ of optimum on average and $98.4\\%$ on the best run. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method. Using a sparse CSR representation, the same approach scales to G-set instances with up to $20{,}000$ vertices reducing memory requirements by up to $3333\\times$ while maintaining a consistent improvement over the CMG warm start. Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: OPT2026 (Neurips Workshop)",
  "arxiv": "2610.19043",
  "author_total": 10,
  "authors": [
    {
      "name": "M. Harper Langston"
    },
    {
      "name": "Pierre-David Letourneau"
    },
    {
      "name": "Dalton Jones"
    },
    {
      "name": "Harris Teague"
    },
    {
      "name": "Peter Scott"
    },
    {
      "name": "Mingu Lee"
    },
    {
      "name": "Richard Lethin"
    },
    {
      "name": "Chris Lott"
    },
    {
      "name": "Roland Memisevic"
    },
    {
      "name": "Fatih Porikli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30qgvvrzge47y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19043",
  "fulltext_url": null,
  "id": "30qgvvrzge47y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19043",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7222277354",
  "pdf_url": "https://arxiv.org/pdf/2610.19043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30qgvvrzge47y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT",
  "title_text": "Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/30qgvvrzge47y",
  "venue": "arXiv",
  "versions": []
}