Lower bounds of annealing schedule for Boltzmann and Cauchy machines

The authors explore the requirements for an annealing schedule that guarantees fast convergence. These conditions are then tailored to both the Boltzmann and Cauchy machines. Using these conditions, the authors derive an annealing schedule that is a lower bound for the previously developed annealing schedules of the Boltzmann and Cauchy machines. It is shown that various annealing schedules can be derived from the so-called kernel sequence. In this way, it is possible to unify the various annealing schedules by the kernel sequence and focus attention on the kernel sequence only. The authors present experimental results for a typical cost function and compare the advantages and disadvantages of the new algorithms with those of two other annealing schedules.<>