# Max–min inequality

In mathematics, the **max–min inequality** is as follows: for any function *f*: *Z* × *W* → ℝ,

When equality holds one says that *f*, *W* and *Z* satisfies a strong max–min property (or a saddle-point property). As the function *f*(*z*,*w*)=sin(*z*+*w*) illustrates, this equality does not always hold. A theorem giving conditions on *f*, *W* and *Z* in order to guarantee the saddle point property is called a minimax theorem.

## Proof

Define .

## References

- Boyd, Stephen; Vandenberghe, Lieven (2004),
*Convex Optimization*, Cambridge University Press

## See also

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