{
  "id": "2409.08119",
  "version": "v1",
  "published": "2024-09-12T15:09:07.000Z",
  "updated": "2024-09-12T15:09:07.000Z",
  "title": "Duality theory in linear optimization and its extensions -- formally verified",
  "authors": [
    "Martin Dvorak",
    "Vladimir Kolmogorov"
  ],
  "comment": "Code: https://github.com/madvorak/duality/tree/v2.0.0",
  "categories": [
    "math.OC",
    "cs.LO"
  ],
  "abstract": "Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take ``infinite values''.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T15:09:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear optimization",
      "extensions",
      "extend duality theory",
      "linear combination",
      "infinite values"
    ],
    "tags": [
      "github project"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}