Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:field |
optimization
linear algebra |
| gptkbp:generalizes |
Fourier–Motzkin elimination
|
| gptkbp:hasApplication |
feasibility of linear systems
proofs of strong duality |
| https://www.w3.org/2000/01/rdf-schema#label |
Farkas' lemma
|
| gptkbp:namedAfter |
gptkb:Gyula_Farkas
|
| gptkbp:publishedIn |
1894
|
| gptkbp:relatedTo |
separation theorems
duality in optimization theory of linear inequalities |
| gptkbp:sentence |
Given a matrix A and vector b, exactly one of the following holds: (1) There exists x ≥ 0 such that Ax = b, or (2) There exists y such that y^T A ≥ 0 and y^T b < 0.
|
| gptkbp:usedIn |
convex analysis
duality theory linear programming |
| gptkbp:bfsParent |
gptkb:Convex_Analysis
|
| gptkbp:bfsLayer |
6
|