There is some very basic information in the documentation about searching for a global minimum. The point is, fmincon searches for a local minimum, and exit flag = 1 tells you that the solution is indeed a local minimum. But fmincon does not search for a global minimum.
Using MultiStart can be an easy way to search for a global minimum using fmincon as the local solver. But there is never a guarantee that you found the global minimum. You might have some extra information, such as limits on curvature, that can enable you to conclude that a solution is global. But there is nothing built-in. Sorry.
Alan Weiss
MATLAB mathematical toolbox documentation
