{
  "abstract": "We study why the proximal bundle method (PBM) can perform better in practice when it retains more cutting planes. We consider convex objectives with quadratic growth and an unknown piecewise-smooth structure. Our key observation is that retaining sufficiently many cutting planes allows PBM to exploit the objective's piecewise-smooth structure and behave as if it were optimizing a smooth function. We provide a theoretical explanation for the observed linear convergence of PBM on piecewise-smooth objectives when it retains sufficiently many cutting planes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11480",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenwei Lin"
    },
    {
      "name": "Zhe Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c73wk6mzgj3fx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11480",
  "fulltext_url": null,
  "id": "c73wk6mzgj3fx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11480",
  "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"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7212277189",
  "pdf_url": "https://arxiv.org/pdf/2609.11480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c73wk6mzgj3fx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth",
  "title_text": "Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/c73wk6mzgj3fx",
  "venue": "arXiv",
  "versions": []
}