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Max–min inequality — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T22:55:02.305Z
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Max–min inequality — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_86a9cebfcd2f (Metraipolis archive dc_86a9cebfcd2f, sha256 4837ac428997982aab66469dc16acad319a72cf6aee8500d48e61807fcec62c2)

BibTeX

@misc{dc86a9cebfcd2f,
  title = {Max–min inequality — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_86a9cebfcd2f; sha256 4837ac428997982aab66469dc16acad319a72cf6aee8500d48e61807fcec62c2},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the max–min inequality is as follows: For any function f : Z × W → R , {\displaystyle \ f:Z\times W\to \mathbb {R} \ ,} sup z ∈ Z inf w ∈ W f ( z , w ) ≤ inf w ∈ W sup z ∈ Z f ( z , w ) . {\displaystyle \sup _{z\in Z}\inf _{w\in W}f(z,w)\leq \inf _{w\in W}\sup _{z\in Z}f(z,w)\ .} When equality holds one says that f, W, and Z satisfies a strong max–min property (or a saddle-point property). The example function f ( z , w ) = sin ( z + w ) {\displaystyle \ f(z,w)=\sin(z+w)\ } illustrates that the equality does not hold for every function. A theorem giving conditions on f, W, and Z which guarantee the saddle point property is called a minimax theorem.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Max–min inequality» — https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality
Wikidata Q6796210 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q6796210
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Max%E2%80%93min_inequality?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1315046408, consultata il 2026-10-07T22:31:42.497Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 4a16a3e511d42b6a6b347de82901c26eb80a5dc0a2d25c8af527a2ff7ccdf996