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

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

[a1]	J. Szép, F. Forgó, "Introduction to the theory of games" , Reidel (1985) pp. Sect. 9.1
[a2]	R.J. Thierauf, R.A. Grosse, "Decision making through operations research" , Wiley (1970) pp. Chapt. 3
[a3]	J.K. Sengupta, "Stochastic optimization and economic models" , Reidel (1986) pp. Chapt. IV
[a4]	T.J. Rivlin, "An introduction to the approximation of functions" , Dover, reprint (1981)