We discuss the asymptotic behavior of time-inhomogeneous Metropolis chains for solving constrained sampling and optimization problems. In addition to the usual inverse temperature schedule , the type of Markov processes under consideration is controlled by a divergent sequence of parameters...

We establish that the min-sum message-passing algorithm and its asynchronous variants converge for a large class of unconstrained convex optimization problems, generalizing existing results for pairwise quadratic optimization problems. The main sufficient condition is that of scaled diagonal...