Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
topological vector spaces
convex-concave functions |
| gptkbp:field |
gptkb:mathematics
functional analysis game theory |
| gptkbp:generalizes |
von Neumann's minimax theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sion's minimax theorem
|
| gptkbp:namedAfter |
Maurice Sion
|
| gptkbp:publicationYear |
1958
|
| gptkbp:publishedIn |
gptkb:Pacific_Journal_of_Mathematics
|
| gptkbp:sentence |
If X is a compact convex subset of a linear topological space, Y is a convex subset of a linear topological space, and f : X × Y → ℝ is such that f(·, y) is upper semicontinuous and convex for each y in Y, and f(x, ·) is lower semicontinuous and concave for each x in X, then min_x max_y f(x, y) = max_y min_x f(x, y).
|
| gptkbp:usedIn |
economics
mathematical analysis optimization theory |
| gptkbp:bfsParent |
gptkb:Toland's_theorem
gptkb:Minimax_theorem |
| gptkbp:bfsLayer |
7
|