{
  "abstract": "We propose a safeguarded Anderson-accelerated subgradient extragradient method for variational inequalities in real Hilbert spaces. The method combines classical projection onto the feasible set with an explicit projection onto a supporting half space and finite memory Anderson correction. A self-adaptive step size with a summable additive recovery sequence is used without prior knowledge of the Lipschitz constant. Weak convergence is established under a solution-oriented condition that does not require monotonicity or pseudomonotonicity. Under a local projection-residual error bound, we obtain Q-linear convergence of the distance to the solution set and strong R-linear convergence of the iterates without assuming uniqueness. Numerical experiments on a dense nonlinear orthogonal transform variational inequality, and a dense nonlinear network consensus model illustrates the performance of the method.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0001, South Africa",
    "Department of Mathematics, Durban University of Technology, Durban 4000, South Africa",
    "School of Agriculture and Science, University of KwaZulu-Natal, Durban 4000, South Africa"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Austine Efut Ofem",
      "orcid": "0000-0001-8064-2326"
    },
    {
      "affs": [
        1
      ],
      "name": "Adhir Maharaj"
    },
    {
      "affs": [
        2
      ],
      "name": "Virath Singh",
      "orcid": "0000-0002-5794-5350"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97pb07fa2ngqf.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193633",
  "fulltext_url": null,
  "id": "97pb07fa2ngqf",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3633",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7221026074",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/97pb07fa2ngqf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193633",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3633"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method",
  "title_text": "Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/97pb07fa2ngqf",
  "venue": "Mathematics",
  "versions": []
}