{
  "abstract": "This paper presents Peppy, an AI-assisted workflow for discovering tight, analytic convergence proofs for first-order optimization algorithms. Generic approaches to using LLMs to conduct mathematical research target an unspecified, broad spectrum of problems and sometimes use the Lean 4 proof assistant for formalization. On the other hand, Peppy leverages domain-specific knowledge more heavily and is thereby capable of constructing the proofs in a more structured manner, which allow a minimal and accessible verification through SymPy. We experimentally demonstrate through examples that Peppy provides a rigorous, practical, and reproducible paradigm for AI-assisted theorem synthesis in optimization. We further highlight its capability of closing several open problems on tight convergence analysis of first-order optimization algorithms, including conjectures for Nesterov's FGM. Overall, Peppy is designed to turn the art of optimization algorithm analysis into a science.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35762",
  "author_total": 5,
  "authors": [
    {
      "name": "Jaewook J. Suh"
    },
    {
      "name": "TaeHo Yoon"
    },
    {
      "name": "Edward Duc Hien Nguyen"
    },
    {
      "name": "Bicheng Ying"
    },
    {
      "name": "Shiqian Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq86979m42ek4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35762",
  "fulltext_url": null,
  "id": "eq86979m42ek4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35762",
  "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",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214711889",
  "pdf_url": "https://arxiv.org/pdf/2609.35762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq86979m42ek4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:20Z",
      "native_id": "2609.35762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms",
  "title_text": "Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:20Z",
  "url": "https://research.draconitic.com/paper/eq86979m42ek4",
  "venue": "arXiv",
  "versions": []
}