Max-min inequality

Max-min inequality

In mathematics, the max-min inequality is as follows. For any function f : R^n \times R^m and any W \subseteq R^n, Z \subseteq R^m,


\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,V satisfies the strong max-min property or the saddle-point property.

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