I am trying to maximize a function $f(x)$ of a vector of reals $x=<x_1, x_2, ...x_n>$. In my practical application, I have no expression for $f$ whatsoever, all I can do is given a vector $x$, calculate $f(x)$ via a deterministic experiment.
So, instead of having to set a step size $\alpha$, calculate derivatives, etc, just see whether the move $x_1 ->x_1(1+\alpha)$ increases $f$, or $x_1 ->x_1(1-\alpha)$ increases it, transform $x_1$ accordingly, and then iterate over all coordinates in this manner until some termination criterium is met. Here $\alpha$ is a small positive number like $0.05$.
This is more practical for me than a standard gradient descent, because the value of $f$ is completely different order of magnitude of the $x_i$s, as well its derivative, so it will be harder to choose appropriate step size in a classical text book gradient descent manner.
Does this approach make sense? Does it have a specific name?