{
  "abstract": "We study second-order fixed-ray Dini sensitivity of the efficient solution map \\(S\\) for the parametric vector problem \\(\\min_C f(p,x)\\) subject to \\(x\\in H(p)\\). Under a value-to-decision error bound (VDB) -- an inverse stability estimate -- the second-order semi-derivative of the marginal map \\(Φ\\) transfers to an exact second-order Dini formula for \\(S\\). The result separates value sensitivity from the inverse recovery of efficient decisions. This mechanism allows a nonsingleton efficient-value fiber and requires neither injectivity nor strict monotonicity of \\(\\nabla_x f\\). For structured feasible maps \\(H(p)=\\{x\\inΩ: g(p,x)\\in D\\}\\), we derive primitive-data formulas for \\(D^2H\\), \\(D^2Φ\\), and \\(D^2S\\) under Robinson metric regularity, second-order regularity of \\(Ω\\) and \\(D\\), objective-aware recession conditions, and directional second-order semi-derivability of the data. Polyhedral inequality/equality systems give explicit specializations. A parametric multi-objective portfolio family verifies (VDB) with an explicit constant, obtained directly from the model's feasible directions, while a two-branch example shows how the formula operates on a nonsingleton decision fiber.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.28965",
  "author_total": 2,
  "authors": [
    {
      "name": "N. X. D. Bao"
    },
    {
      "name": "Tan H. Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11dtg35phzde8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.28965",
  "fulltext_url": null,
  "id": "11dtg35phzde8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.28965",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7166740057",
  "pdf_url": "https://arxiv.org/pdf/2606.28965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11dtg35phzde8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2606.28965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.28965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Second-Order Sensitivity of Efficient Solution Maps in Parametric Vector Optimization with Set Constraints",
  "title_text": "Second-Order Sensitivity of Efficient Solution Maps in Parametric Vector Optimization with Set Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/11dtg35phzde8",
  "venue": "arXiv",
  "versions": []
}