{
  "abstract": "We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an application, we use our framework to study the weighted low-rank approximation. We also provide numerical validation of our convergence results on the image completion task.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30885",
  "author_total": 2,
  "authors": [
    {
      "name": "Conglong Xu"
    },
    {
      "name": "Hao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/08xqpbw3xcst4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30885",
  "fulltext_url": null,
  "id": "08xqpbw3xcst4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30885",
  "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"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7214577710",
  "pdf_url": "https://arxiv.org/pdf/2609.30885",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/08xqpbw3xcst4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30885",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30885"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Retraction-Based Gradient Projection Algorithms on Manifolds",
  "title_text": "Retraction-Based Gradient Projection Algorithms on Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/08xqpbw3xcst4",
  "venue": "arXiv",
  "versions": []
}