Max–min inequality
In mathematics, the max–min inequality is as follows: for any function ,
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 (PDF), Cambridge University Press
See also
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