Gale’s theorem on linear inequalities
E612748
Gale’s theorem on linear inequalities is a fundamental result in convex geometry and linear programming that characterizes the solvability of systems of linear inequalities via an associated alternative system.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gale’s theorem on linear inequalities canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in convex geometry ⓘ result in linear programming ⓘ |
| alsoKnownAs | Gale’s theorem of alternatives NERFINISHED ⓘ |
| appliesTo |
feasibility problems in linear programming
ⓘ
systems of linear inequalities ⓘ |
| category |
theorem in functional analysis
ⓘ
theorem in real analysis ⓘ |
| characterizes | solvability of systems of linear inequalities ⓘ |
| concerns |
existence of solutions to linear inequalities
ⓘ
infeasibility certificates for linear systems ⓘ |
| field |
convex geometry
ⓘ
linear programming ⓘ optimization theory ⓘ |
| framework | finite-dimensional real vector spaces ⓘ |
| gives | necessary and sufficient conditions for solvability of linear inequalities ⓘ |
| hasConcept |
alternative system
ⓘ
certificate of infeasibility ⓘ primal–dual relationship ⓘ |
| implies | mutual exclusivity of primal and alternative systems ⓘ |
| influenced | modern formulations of linear programming duality ⓘ |
| involves |
convex cones
ⓘ
homogeneous linear inequalities ⓘ nonhomogeneous linear inequalities ⓘ separation properties of convex sets ⓘ |
| isPartOf |
classical theory of linear inequalities
ⓘ
foundations of mathematical economics ⓘ |
| logicalForm | either-or alternative theorem NERFINISHED ⓘ |
| mathematicianAssociated | David Gale NERFINISHED ⓘ |
| namedAfter | David Gale NERFINISHED ⓘ |
| provides | alternative system of linear inequalities ⓘ |
| relatedTo |
Farkas’ lemma
NERFINISHED
ⓘ
Gordan’s theorem NERFINISHED ⓘ Hahn–Banach separation theorem NERFINISHED ⓘ Stiemke’s theorem NERFINISHED ⓘ convex separation theorems ⓘ theorems of the alternative ⓘ |
| typeOf |
duality statement
ⓘ
separation theorem ⓘ |
| usedAs |
tool for analyzing feasibility regions
ⓘ
tool for proving existence of equilibria ⓘ |
| usedIn |
duality theory in linear programming
ⓘ
economic equilibrium theory ⓘ feasibility analysis of linear systems ⓘ game theory ⓘ proofs of strong duality in linear programming ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.