Laws of large numbers for the annealing algorithm (Q751733)

A convergence of the algorithm of simulated annealing is considered. First, an error in the paper of \textit{B. Gidas} [J. Stat. Phys. 39, 73-131 (1985; Zbl 0642.60049)] is pointed out. Next, well-known laws of large numbers for time-inhomogeneous Markov chains are applied. Assumptions formulated in terms of Dobrushin contraction coefficients lead to appropriate cooling constant. Namely, in the cooling scheme \(\beta (n)=\gamma \log n\) weak LLN holds for \(\gamma <\gamma_ 0\) and strong LLN holds for \(\gamma <\gamma_ 0/2\) with some given \(\gamma_ 0\).