I have a function $f(x_1, x_2, \ldots, x_n)$. Here $x_i $ are real variables and $f$ is also real. I tried such a method for finding the minimum of $f$.
First, let us fix $x_2$ to $x_n$, and find the $x_1$ that minimizes $f$. Then, let us fix all $x_i$ other than $x_2$, and find the $x_2$ that minimizes $f$. Next we turn to $x_3$, and so on.
It is observed that $f$ decays in a power law way (very slow) towards the minimum.
The question is, what kind of function has this behavior? In my case, the function $f$ has no explicit expression, it is like a black box.
It is not hard to see that if $f$ is a quadratic function, then it will decay exponentially towards the minimum.