Argmax

math

Definition

Argmax

$\arg \max$ is the argument of the maxima of a function.

Given a set $S\subseteq D_f$, the $\arg \max$ for an argument $x\in S$ for a function $f:D_f\to Y$ is defined as:

$$\arg \underset{x\in S}{\max }f(x):=\{x\in S:f(s)\le f(x)\forall s\in S\}$$