Not in the general case, no. It can be shown in theory that there are functions whose global minimum can only be known numerically by testing every floating point number in a range. For example you can use a Dirac delta function to introduce an arbitrary reduction in value, and no numeric process would be able to tell unless it just happens to exactly match the location.
In order to get global minima you generally need Calculus at the very least, and sometimes much much more sophisticated analysis.
There are some functions that have been studied for centuries and all that is proved so far is that there exists at least one root less than 10^300000 and that it has an infinite number of roots (proving that the function had a root at all was a pretty big achievement.)
