{
  "abstract": "We provide an increasing approximating sequence of smooth lower bounds for the minimum of n ≥ 2 $n\\geq 2$ real numbers, with exponential convergence. For any given strict lower bound, we obtain a strict improvement through a harmonic increment. Additionally, we compute the maximum relative and absolute errors and construct a smooth approximating sequence from above using the geometric mean. Closed-form expressions are provided for the case n = 2 $n = 2$ , where the solution relates to the well-known crossed-ladders problem.",
  "abstract_shown": true,
  "affiliations": [
    "Chair of Operations, Economics and Strategy, École Polytechnique Fédérale de Lausanne"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Thomas A. Weber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0f51sdebawaxr.bib",
  "cited_by": 0,
  "doi": "10.1186/s13660-026-03519-3",
  "fulltext_url": "https://doi.org/10.1186/s13660-026-03519-3",
  "id": "0f51sdebawaxr",
  "issns": [
    "1029-242X"
  ],
  "landing_url": "https://doi.org/10.1186/s13660-026-03519-3",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
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  "openalex": "W7171502830",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "SpringerOpen",
  "ris": "https://research.draconitic.com/paper/0f51sdebawaxr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:46:36Z",
      "native_id": "c2e175b4305d443eac9c64b0c1ea4295",
      "source": "doaj",
      "url": "https://doi.org/10.1186/s13660-026-03519-3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematical Inequalities and Applications",
      "subfield": "general"
    }
  ],
  "title": "Smooth approximation of the minimum function from below (and above)",
  "title_text": "Smooth approximation of the minimum function from below (and above)",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:46:36Z",
  "url": "https://research.draconitic.com/paper/0f51sdebawaxr",
  "venue": "Journal of Inequalities and Applications",
  "versions": []
}