# Arg max

The notation

**arg max** (or

**argmax**) in mathematical descriptions stands for the

**argument of the maximum**, that is to say, the value of the given

argument for which the value of the given expression attains its

maximum value. This is well-defined only if the maximum is reached at a single value. Thus

holds

if and only if *x*_{0} is the unique value of

*x* for which

*f*(

*x*) is maximized.

**arg min** (or **argmin**) is defined analogously.