{
  "abstract": "In this paper, we study the computational complexity of finding fixed points for set-valued contractions. We first formulate a computational problem for Nadler's fixed-point theorem: Projected-Nadler, and prove that it is $\\mathsf{CLS}$-complete by showing its equivalence to Continuous-LocalOpt. We then establish a stronger converse for Nadler's fixed point theorem that can be applied as a tool to analyze the convergence rate of set-valued basic iteration procedure. Finally, we reduce large-margin triplet stationarity problem to Projected-Nadler. Together with its $\\mathsf{CLS}$-hardness introduced in [arXiv:2509.16898], this yields $\\mathsf{CLS}$-completeness of large-margin triplet stationarity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14101",
  "author_total": 2,
  "authors": [
    {
      "name": "Emmanouil-Vasileios Vlatakis-Gkaragkounis"
    },
    {
      "name": "Pucheng Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87x8tzyze1a9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14101",
  "fulltext_url": null,
  "id": "87x8tzyze1a9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14101",
  "language": null,
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  "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.CC"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2608|Fixed Point Theorems Analysis"
    ]
  ],
  "openalex": "W7213373588",
  "pdf_url": "https://arxiv.org/pdf/2609.14101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87x8tzyze1a9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.14101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Complexity of Finding Fixed Points for Set-Valued Contractions",
  "title_text": "On the Complexity of Finding Fixed Points for Set-Valued Contractions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:26Z",
  "url": "https://research.draconitic.com/paper/87x8tzyze1a9g",
  "venue": "arXiv",
  "versions": []
}