Argmin

math

Definition

Argmin

$\arg \min$ is the argument of the minima of a function.

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

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