{
  "abstract": "Motivated by sparse principal component analysis (PCA), this paper proposes ATE-ManPG, a safeguarded transport-extrapolated proximal gradient method for minimizing the sum of a smooth function and a convex, possibly nonsmooth function over the Stiefel manifold. The method augments the manifold proximal gradient method (ManPG) with two ingredients: momentum obtained by transporting the previous proximal search direction to the current tangent space, protected by a monotone restart safeguard, and a bounded adaptive proximal parameter. For the exact idealized iteration, global convergence to stationary points and O(1/ε2) iteration complexity are proved; under a proximal Kurdyka–Łojasiewicz condition with exponent 1/2 and a relative-error condition, both stated as explicit hypotheses, the convergence is R-linear. Experiments on a sparse-PCA model, validated by an external residual certificate at the returned point, show a 3.6× mean iteration-count reduction relative to fixed-parameter ManPG; a factorial ablation attributes most of this reduction to the adaptive parameter, while transported momentum adds a further 6.4% on average, concentrated in one paired trial.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China",
    "National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Chuanjun Yan"
    },
    {
      "affs": [
        1
      ],
      "name": "Lin Chen",
      "orcid": "0000-0003-4330-1519"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9jzrt6r6kcpk.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15110828",
  "fulltext_url": null,
  "id": "f9jzrt6r6kcpk",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/11/828",
  "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": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/f9jzrt6r6kcpk.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T00:21:06Z",
      "native_id": "10.3390/axioms15110828",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/11/828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold",
  "title_text": "A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T00:21:04Z",
  "url": "https://research.draconitic.com/paper/f9jzrt6r6kcpk",
  "venue": "Axioms",
  "versions": []
}