Hi! I was given a problem to solve, which boils down to finding the arguments that minimize some function 'f(a, b)', that is, if we have 'y = f(a, b)', I need to find the values of 'a' and 'b' that will make 'y' as small as possible. My main problem is the fact that the function is unknown, but it can be evaluated (approximately) for any given pair of arguments. I have a simple idea, but it usually finds local minima, while what I need is the global minimum. Can anyone please help me out?

It's not possible for a generic function to find the global minimum without evaluating it for all possible arguments - simply because it could be anywhere.
However, if you know a little more about the function (like it's gradient), you can usually find a pretty good approximation to the real minimum. Gradient walks, threshold algorithms and tempering come to mind. As always, google and wikipedia should be a good help on these.

Helpful keywords may be "black-box function" and "no-free-lunch theorem".
Regards!