Suppose we need to design a system f(x) with parameter x according to some criterion T, and we do not have an analytic expression of f(x), but we know that if we increase x, then f(x) is also non-linearly increased. A solution can be obtained via:
1) initial guess of x,
2) obtain f(x),
3) if f(x)>T, decrease x, go to 2),
4) else, stop, output x.
We call the above a heuristic method or an empirical method?