I have a fitness function $f(x,y)$, which I am sampling at discrete $x$ and $y$ in order to minimize $f$. In addition to the location of the minimum, I would like to give an appropriate measure of confidence or quality of the determined location, so that I can detect if the minimum is rather wide, or if $f$ is non-convex.
Without making further assumptions about $f$, what would be an appropriate measure of quality?