As the title says, the mathematical expression which is the input to the integral is called the "integrand". Is there a comparable term for the infimum? (and/or supremum). That is, what would I call this term?
$$ \inf_{x \in S}\left\{ \underbrace{f(x) + g(x) }_{???} \right\} $$
The '-nd' suffix of the words integrand, summand, multiplicand etc is the gerund form, meaning "that which is to be integrated/summed/multiplied/etc". As such, there may be a case for the words infimand and supremand for these two functions, but presently they are not words.
Personally, I'd define $f$ and $g$ first and then that "we take the infimum of their sum".