I have a pretty simple function that I want to express, but I'm having trouble coming up with a pleasing notation to express it. The function is:
$h(y) = \arg \min_x |f(x, y)|$
$g(y) = f(h(y), y)$
In English, "$g$ is the value of $f$ at which its absolute value is minimized". Is there a standard symbol for this sort of thing, or a more compact notational representation that I'm missing?