{
  "abstract": "Second-order methods for smooth monotone variational inequalities reach the optimal rate $O(T^{-3/2})$, but a distributed exact Jacobian costs $d$ times more communication than an operator value. We show that similarity does part of the work for free: if the server's Jacobian differs from the global one by at most $β$, using it gives $O(L_1D^3T^{-3/2}+βD^2T^{-1})$ at first-order communication cost. A quasi-Newton approximation of the residual Jacobian $\\nabla F-\\nabla F_1$, built from secants already communicated, improves the model but cannot remove the $T^{-1}$ term, because any uniform bound on the Jacobian error leaves it in the rate. We therefore certify the surrogate only along the candidate step: one Jacobian-vector product tests it, and a failed test is reused as an exact correction. This attains the exact rate $O(L_1D^3T^{-3/2})$ while transmitting only vectors. Experiments on LIBSVM and synthetic instances measure accuracy against communication.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22481",
  "author_total": 6,
  "authors": [
    {
      "name": "Ewsey R. Obzherin"
    },
    {
      "name": "Roman M. Mozhaev"
    },
    {
      "name": "Alexander V. Gasnikov"
    },
    {
      "name": "Martin Takáč"
    },
    {
      "name": "Artem A. Agafonov"
    },
    {
      "name": "Dmitry I. Kamzolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feh1pt7bjwwcd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22481",
  "fulltext_url": null,
  "id": "feh1pt7bjwwcd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22481",
  "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",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214031842",
  "pdf_url": "https://arxiv.org/pdf/2609.22481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feh1pt7bjwwcd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Certified Residual Quasi-Newton Methods for Distributed Variational Inequalities",
  "title_text": "Certified Residual Quasi-Newton Methods for Distributed Variational Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/feh1pt7bjwwcd",
  "venue": "arXiv",
  "versions": []
}