{
  "abstract": "We study multiblock convex--concave saddle-point problems of the form $\\min_x\\max_y\\{f(x)+H(x,y)-g(y)\\}$, with separately charged partial-gradient oracles for all three objective components. We impose joint smoothness and strong convexity bounds on the functions $f$ and $g$, together with blockwise Lipschitz conditions on the partial gradients of $H$, so that the resulting oracle complexities reflect the smoothness and dependency parameters specific to each oracle. Under strong convexity, we develop a randomized lifted extragradient method that achieves linear convergence while providing simultaneous complexity guarantees for all oracles. The partial-gradient complexities for $f$ and $g$ exhibit the expected square-root dependence on the corresponding block condition numbers, whereas the coupling-gradient complexities depend on the associated curvature-normalized smoothness parameters. Finite-dimensional bilinear subclasses provide lower-complexity benchmarks within a randomized blockwise linear-span model. When strong convexity of $f$ and $g$ is not assumed, a regularization argument yields expected restricted-gap guarantees with accuracy dependence $\\varepsilon^{-1/2}$ for the objective-gradient oracles and $\\varepsilon^{-1}$ for the coupling-gradient oracles, up to logarithmic factors. Experiments show observed oracle savings and runtime improvements in regimes of poor objective conditioning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12656",
  "author_total": 5,
  "authors": [
    {
      "name": "Nhat Trung Nguyen"
    },
    {
      "name": "Ivan Dorofeev"
    },
    {
      "name": "Irina Podlipnova"
    },
    {
      "name": "Yuriy Dorn"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mw0d3tj99vhe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12656",
  "fulltext_url": null,
  "id": "7mw0d3tj99vhe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12656",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.12656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mw0d3tj99vhe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Complexity of Multiblock Convex-Concave Saddle-Point Problems with General Smooth Coupling",
  "title_text": "Complexity of Multiblock Convex-Concave Saddle-Point Problems with General Smooth Coupling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/7mw0d3tj99vhe",
  "venue": "arXiv",
  "versions": []
}