{
  "abstract": "The infimal displacement vector of the nonexpansive operator underlying the primal-dual hybrid gradient algorithm (PDHG) is known to encode useful information for infeasible optimization problems. In particular, for the ellipsoid separation problem (ESP), where the goal is to find a separating hyperplane between two collections of ellipsoids, the infimal displacement vector corresponding to an infeasible second-order cone program (SOCP) encodes a separating hyperplane. We show FISTA computes a sequence of approximations to the dual component of the infimal displacement vector and establish that a solution to the ESP can be obtained in $\\mathcal{O}(δ_{\\mathcal{A}}^{-2})$ iterations. Here $δ_{\\mathcal{A}}$ denotes the distance between the convex hulls of the two ellipsoid collections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33902",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew Hough"
    },
    {
      "name": "Stephen A. Vavasis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79x1sge3ky248.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33902",
  "fulltext_url": null,
  "id": "79x1sge3ky248",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33902",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7223861325",
  "pdf_url": "https://arxiv.org/pdf/2610.33902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79x1sge3ky248.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Ellipsoid Separation in Data-Dependent Time via Infimal Displacement Vectors",
  "title_text": "Ellipsoid Separation in Data-Dependent Time via Infimal Displacement Vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/79x1sge3ky248",
  "venue": "arXiv",
  "versions": []
}