{
  "abstract": "In the present paper, a study is made of first-order differential properties of certain multifunctions, which are defined as a solution map associated with a family of parameterized ``split\" feasibility problems. The latter are a class of convex feasibility problems, whose specific structure makes them suitable for well-established applications in several areas of engineering and systems biology. As a result, inner and outer approximations of the graphical (contingent) derivative of the solution map are provided, which are expressed in terms of derivatives of the problem data. As an application, a perspective is also discussed for employing some of these achievements in the formulation of optimality conditions for mathematical programs with ``split\" feasibility constraints.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28319",
  "author_total": 1,
  "authors": [
    {
      "name": "Amos Uderzo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bz2p27qwhfebf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28319",
  "fulltext_url": null,
  "id": "bz2p27qwhfebf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28319",
  "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": "W7204771883",
  "pdf_url": "https://arxiv.org/pdf/2608.28319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bz2p27qwhfebf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "First-order approximations of multifunctions defined implicitly by \"split\" feasibility problems with applications to optimization",
  "title_text": "First-order approximations of multifunctions defined implicitly by \"split\" feasibility problems with applications to optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/bz2p27qwhfebf",
  "venue": "arXiv",
  "versions": []
}