{
  "abstract": "We prove that the weak Pareto solution set of a multi-objective optimization problem with convex polynomial objectives and constraints is connected, assuming neither boundedness of the constraint set nor a constraint qualification. Since this set is semi-algebraic, its connectedness implies that it is path-connected whenever it is nonempty. In particular, convex quadratic multi-objective optimization problems have connected weak Pareto solution sets; this answers the weak Pareto part of an open question posed by N.~D.~Yen in \\emph{Recent Developments in Vector Optimization} (Springer, 2012).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01029",
  "author_total": 1,
  "authors": [
    {
      "name": "Vu Trung Hieu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/136fq8j329b5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01029",
  "fulltext_url": null,
  "id": "136fq8j329b5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01029",
  "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": "W7216484956",
  "pdf_url": "https://arxiv.org/pdf/2610.01029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/136fq8j329b5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A connectedness result for convex polynomial multi-objective optimization without boundedness",
  "title_text": "A connectedness result for convex polynomial multi-objective optimization without boundedness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/136fq8j329b5g",
  "venue": "arXiv",
  "versions": []
}