On the Convergence Rate of Annealing Processes

Abstract

For the class of inhomogeneous Markov processes arising from simulated annealing, it is shown that ${{\lim _{t \to \infty } P(X_t = i)} / {\exp ({{ - u(i)} / {T(t)}})}}$ exists and is positive for each state i, where $T(t)$ is the temperature and $u(i)$ is the energy level at i (assuming that min; $u(i) = 0$). The method used is to consider the Forward equations associated with such processes.