{
  "abstract": "We establish near-optimal higher-order oracle bounds for smooth monotone variational inequalities. For fixed $p\\ge2$, let $F$ be monotone on a known compact convex set $X$ of diameter at most $D$, with $\\operatorname{Lip}(D^{p-1}F)\\le L_p$. Each feasible query returns the complete jet $(F,DF,\\ldots,D^{p-1}F)$, and the goal is to find $x$ with tangent residual $\\operatorname{dist}(0,F(x)+N_X(x))\\le\\varepsilon$. Writing $Q=L_pD^p/\\varepsilon$, we improve the $\\widetilde O_p(Q^{1/p})$ upper bound of Chen et al. to $\\widetilde O_p(Q^{2/(3p-1)})$ via a dimension-independent deterministic algorithm that returns an explicit tangent-residual certificate. We prove a matching $Ω_p(Q^{2/(3p-1)})$ lower bound for arbitrary adaptive deterministic algorithms and randomized algorithms with per-instance success probability at least $2/3$, without span or tensor-update restrictions. Hence the high-dimensional worst-case oracle complexity is $\\widetildeΘ_p((L_pD^p/\\varepsilon)^{2/(3p-1)})$. The same method applies to smooth convex--concave minimax problems, improving the fixed-geometry accuracy exponent from $4/(3p+1)$ to $2/(3p-1)$ and matching the known lower-bound exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13462",
  "author_total": 6,
  "authors": [
    {
      "name": "Haihan Zhang"
    },
    {
      "name": "Wendao Wu"
    },
    {
      "name": "Chenheng Zhang"
    },
    {
      "name": "Cong Fang"
    },
    {
      "name": "Haoxuan Li"
    },
    {
      "name": "Zhouchen Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcz4nyw7b6w45.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13462",
  "fulltext_url": null,
  "id": "dcz4nyw7b6w45",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13462",
  "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": "W7213353210",
  "pdf_url": "https://arxiv.org/pdf/2609.13462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcz4nyw7b6w45.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.13462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Matching Higher-Order Oracle Complexity for Smooth Monotone Variational Inequalities",
  "title_text": "Matching Higher-Order Oracle Complexity for Smooth Monotone Variational Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dcz4nyw7b6w45",
  "venue": "arXiv",
  "versions": []
}