{
  "abstract": "ALDER, a single-loop augmented-Lagrangian damped extragradient method, is proposed for smooth nonconvex--concave minimax problems with nonlinear coupled inequality constraints. Within an augmented-Lagrangian framework, ALDER combines prediction--correction steps for the primal variables with explicit projected-and-relaxed multiplier updates in a single loop. The penalty parameter is fixed throughout each run, eliminating inner-loop subproblem solves and iterative penalty updates. We establish uniform boundedness of the relaxed multiplier sequence and, under an extended Mangasarian--Fromovitz constraint qualification, boundedness of the projected output multiplier. Building on these bounds, we show that ALDER finds an $\\varepsilon$-KKT point within $\\mathcal{O}(\\varepsilon^{-7/2})$ complete first-order oracle evaluations in the strongly concave setting and $\\mathcal{O}(\\varepsilon^{-4})$ in the concave setting. These bounds improve upon the best known complexity bounds for multi-loop algorithms for this problem class, achieved by FAL, by removing a $\\log(1/\\varepsilon)$ factor, while retaining a single-loop update structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00691",
  "author_total": 4,
  "authors": [
    {
      "name": "H. Zhang"
    },
    {
      "name": "M. Zhang"
    },
    {
      "name": "Z. Xu"
    },
    {
      "name": "Y. -H. Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29nwvavbgfwps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00691",
  "fulltext_url": null,
  "id": "29nwvavbgfwps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00691",
  "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.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29nwvavbgfwps.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "ALDER: A Single-Loop Augmented-Lagrangian Damped Extragradient Method for Nonconvex--Concave Minimax Problems with Nonlinear Coupled Constraints",
  "title_text": "ALDER: A Single-Loop Augmented-Lagrangian Damped Extragradient Method for Nonconvex--Concave Minimax Problems with Nonlinear Coupled Constraints",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/29nwvavbgfwps",
  "venue": "arXiv",
  "versions": []
}