{
  "abstract": "This paper addresses the problem of designing distributed optimization algorithms. Different to existing methods that usually give sufficient conditions and conservative convergence rates, we propose a framework for determining the exact worst-case convergence rate. The worst-case convergence is defined over the set of $μ$-strongly convex and $L$-Lipschitz objective functions and the set of connected graphs with given algebraic connectivity. Focusing on the Distributed Inexact Gradient Tracking (DIGing)--an algorithm widely deployed in applications and extensively studied in recent years, we develop a systematic design methodology by integrating techniques from graph signal processing and robust control theory. First, we present a novel decomposition structure that enables partial subsystem decoupling. Then we derive explicit formulas for the exact worst-case convergence rate and the corresponding parameters. Numerical experiments validate the correctness and effectiveness of our theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20265",
  "author_total": 3,
  "authors": [
    {
      "name": "Qiuchen Tian"
    },
    {
      "name": "Li Chai"
    },
    {
      "name": "Jinming Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5153zca2xd2b6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20265",
  "fulltext_url": null,
  "id": "5153zca2xd2b6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20265",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5153zca2xd2b6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal Design of Distributed Inexact Gradient Tracking: Exact Worst-case Convergence Rate and Explicit Parameters",
  "title_text": "Optimal Design of Distributed Inexact Gradient Tracking: Exact Worst-case Convergence Rate and Explicit Parameters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/5153zca2xd2b6",
  "venue": "arXiv",
  "versions": []
}