Unless the problem is convex, you won't know if the PSO found the global optimum.

To be certain, you must run complete methods (such as branch and bound) that perform an exhaustive exploration of the search space and prune the subspaces that cannot contain a solution.

Better yet: interval methods can bound the global optimum even in the presence of roundoff errors.

I would say for most mathematical functions, PSO will give a solution nearest to the global minimum.

However, some optimization problems are too complex and maybe non-convex in which case the global minimum solution is also accepted which can be achieved using PSO.