the temperatures $T_i$ decrease exponentially in annealing-time k, i.e., $T_i = T_{i0} \exp(-c_i k^{1/D})$. Of course, the faster the tail of the generating function, the smaller the ratio of acceptance to generated points in the fit. However, in practice, it is found that for a given generating function, this ratio is approximately constant as the fit finds a global minimum. Therefore, for a large parameter space, the efficiency of the fit is determined by the annealing schedule of the generating function.
No rigorous proofs have been given. It is expected that the obvious utility of this algorithm will motivate such proofs. However, actual fits to data are a finite process, and often even only heuristic guides to algorithms that obviously fit many classes of data are important. Heuristic arguments have been given here that this algorithm is faster than the fast Cauchy annealing, where $T_i = T_0/k$, and much faster than Boltzmann annealing, where $T_i = T_0/\ln k$.