Convergence of Simulated Annealing Based Algorithms
I copied this answer from computational science 

There is a theorem that syas that a black box algorithm is guaranteed to find the global minimum of an arbitrary smooth (i.e., twice continuously differentiable) function if and only if it samples points densely in the search space.

Here dense is meant in the topological sense, i.e., it must sample points in arbirarily small neighborhoods of every point.

In this case, the worst case complexity is O((dδ)−n), [the Latex parser chokes with nested big brackets] where d is the diameter of the search space and δ the guaranteed error in x

Edit: While this looks like being the worst case complexity for locating an δ-accurate x rather than for locating a point for a ϵ-accurate f, the complexity for the latter is as bad (even for the rather big value of ϵ=(ffirst−fglobal)/2), as one can easily construct a smooth function which interpolates all data points so far but takes much smaller values in the center of the largest open ball not containing one of the points evaluated.

Thus guaranteed convergence to a global minimum is worthless in practice. (For example, uniformly random search has a convergence guarantee to the global minimizer, whereas most practically fast algorithms don't have one.)

Note that simulated annealing usually performs much worse than modern methods. Rather use code recommended in:

Comparison of derivative-free optimization algorithms (2012, by Nick Sahinidis)

Black-Box Optimization Benchmarking (BBOB) 2012 (by Auger, Hansen, et al.)