{
  "abstract": "Lagrangian duality is fundamental to optimization, from the development of solver techniques to the interpretation of solutions; yet its geometric intuition can be difficult to grasp through mathematical derivation alone. This tutorial explains duality and its implications in a highly visual way for a broad audience of students and practitioners. It develops the motivation for the Lagrangian, the two-player game interpretation, and the connection to Fenchel duality. Throughout, it emphasizes the geometric meaning of the solution from both the primal and dual",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23751",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohini Bariya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ckh6cjvm4nyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23751",
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  "id": "4ckh6cjvm4nyk",
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  "landing_url": "https://arxiv.org/abs/2609.23751",
  "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.HO"
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    [
      "arxiv",
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    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
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  "openalex": "W7214050218",
  "pdf_url": "https://arxiv.org/pdf/2609.23751",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ckh6cjvm4nyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23751",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23751"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Duality in Optimization: A Visual Tutorial",
  "title_text": "Duality in Optimization: A Visual Tutorial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4ckh6cjvm4nyk",
  "venue": "arXiv",
  "versions": []
}