{
  "id": "enwiki-001104062631",
  "slug": "basic-solution-linear-programming",
  "title": "Basic solution (linear programming)",
  "qid": "",
  "lead": "In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P and a vector \\mathbf{x}^* \\in \\mathbb{R}^n , \\mathbf{x}^* is a basic solution if: # All the equality constraints defining P are active at \\mathbf{x}^* # Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \\mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution.",
  "body": "In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P and a vector \\mathbf{x}^* \\in \\mathbb{R}^n , \\mathbf{x}^* is a basic solution if: All the equality constraints defining P are active at \\mathbf{x}^* Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \\mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution. ==References==",
  "categories": [
    "20476732",
    "23468805",
    "26709293"
  ],
  "license": "CC BY-SA 4.0",
  "source_uri": "https://en.wikipedia.org/w/index.php?oldid=1104062631",
  "content_hash": "",
  "created_at": null,
  "updated_at": 1660295406.0,
  "claims": [],
  "contradictions": [],
  "confidence": 0.6,
  "csl": {
    "id": "enwiki-001104062631",
    "type": "webpage",
    "title": "Basic solution (linear programming)",
    "author": [
      {
        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
      }
    ],
    "container-title": "encyclopegia.org",
    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/basic-solution-linear-programming",
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          11
        ]
      ]
    },
    "accessed": {
      "date-parts": [
        [
          2026,
          11,
          11
        ]
      ]
    },
    "license": "CC BY-SA 4.0",
    "DOI": "eo1:enwiki-001104062631",
    "isBasedOn": "https://en.wikipedia.org/w/index.php?oldid=1104062631",
    "note": "Immutable snapshot enwiki-001104062631"
  }
}