Minimax

A mixed extremum

$$\inf_{y\in Y}\sup_{x\in X}F(x,y),\quad\min_{y\in Y}\max_{x\in X}F(x,y),$$

etc. (see also Maximin); it can be interpreted (for example, in decision theory, operations research or statistics) as the least of the losses which cannot be prevented by decision making under the given circumstances.

Comments[edit]

Cf. Minimax statistical procedure for an interpretation in statistics, [a1] for minimaxima in game theory, and [a2], [a3] for a discussion of minimaxima and maximinima in decision theory. Minimax (and maximin) considerations also occur in other parts of mathematics, for instance in approximation theory, [a4].

References[edit]