Given an unknown function $f:\mathbb R^d \to \mathbb R$, we can evaluate its value at any point in its domain, but we don't have its expression. In other words, $f$ is like a black box to us.
What is the name for the problem of finding the minimizer of $f$? What are some methods out there?
What is the name for the problem of finding the solution to the equation $f(x)=0$? What are some methods out there?
In the above two problems, is it a good idea to interpolate or fit to some evaluations of f: $(x_i, f(x_i)), i=1, \dots, n$ using a function $g_\theta$ with known form and parameter $\theta$ to be determined, and then minimize $g_\theta$ or find its root?
Thanks and regards!