{
  "abstract": "We study average consensus over slowly time-varying networks and its application to decentralized optimization. We introduce WAVE, a windowed Chebyshev method that limits the accumulated effect of network variation by restarting the recurrence after finite windows. If $χ$ bounds the network condition number and successive communication operators satisfy $\\|L_{k+1}-L_k\\|\\leqβ$, WAVE reaches $ε$-consensus in $O((\\sqrtχ+\\min\\lbraceβχ^2,χ\\rbrace)\\ln(e/ε))$ communication rounds. This rate matches the fixed-network $\\sqrtχ$ dependence when $β=O(χ^{-3/2})$ and smoothly interpolates across the full range of network variation. For piecewise-constant networks where each change is detected when it occurs and consecutive changes are at least $τ$ rounds apart, WAVE reaches $ε$-consensus in $O((\\sqrtχ+χ/τ)\\ln(e/ε))$ communication rounds. Finally, we use WAVE as the consensus step in an accelerated decentralized optimization method for $α$-smooth convex local objectives with a $μ$-strongly convex average. For sufficiently slow network variation, every agent obtains an $ε$-solution to the global optimization problem after $\\widetilde O(\\sqrt{α/μ}\\,\\sqrtχ)$ communication rounds, matching the fixed-network dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33824",
  "author_total": 6,
  "authors": [
    {
      "name": "Darina Dvinskikh"
    },
    {
      "name": "Anton Novitskii"
    },
    {
      "name": "Demyan Yarmoshik"
    },
    {
      "name": "Alexander Rogozin"
    },
    {
      "name": "Vladislav Matyukhin"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hhzkg6ngnnh0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33824",
  "fulltext_url": null,
  "id": "4hhzkg6ngnnh0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33824",
  "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",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7214788839",
  "pdf_url": "https://arxiv.org/pdf/2609.33824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hhzkg6ngnnh0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Accelerated Consensus and Decentralized Optimization over Slowly Varying Networks",
  "title_text": "Accelerated Consensus and Decentralized Optimization over Slowly Varying Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4hhzkg6ngnnh0",
  "venue": "arXiv",
  "versions": []
}