{
  "abstract": "The paper studies convex minimisation problems involving a composition of a coordinatewise nondecreasing convex function with a finite family of nonnegative, locally Lipschitz continuous and convex functions. We establish complete dual optimality conditions and characterise the entire solution set using multipliers and subgradients associated with a given solution. The results are applied to norm optimisation problems involving minimal time functions with different convex dynamics sets and convex target sets. The sum, maximum and p-norms yield minimal time versions of the Fermat--Torricelli, Chebyshev centre and p-Fermat--Torricelli problems, respectively. Examples in finite and infinite dimensional spaces are provided to illustrate the solution set characterisations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38553",
  "author_total": 2,
  "authors": [
    {
      "name": "Doan Huu Hieu"
    },
    {
      "name": "Nguyen Duy Cuong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wc8hhmvhpjsz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38553",
  "fulltext_url": null,
  "id": "4wc8hhmvhpjsz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38553",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wc8hhmvhpjsz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems",
  "title_text": "Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4wc8hhmvhpjsz",
  "venue": "arXiv",
  "versions": []
}