We expect that as long as the temperature is reduced ``slowly enough,'' i.e. in small enough increments, and allowing time for thermalization at each T, then simulated annealing should allow us to reach the ground state (the optimal solution). But what is ``slow enough''?
Geman and Geman showed that if the temperature is reduced as
for 
large enough (so configurations at 
are close to
random), then we are ``statistically'' guaranteed to find the optimal value.
This means that if we anneal slowly enough, we have a non-trivial probability of obtaining the optimal solution. Thus, if we perform enough different annealings, starting at different random initial configurations, we will eventually obtain an optimal solution.