  This paper studies the convergence properties the well-known message-passing
algorithm for convex optimisation. Under the assumption of pairwise
separability and scaled diagonal dominance, asymptotic convergence is
established and a simple bound for the convergence rate is provided for
message-passing. In comparison with previous results, our results do not
require the given convex program to have known convex pairwise components and
that our bound for the convergence rate is tighter and simpler. When
specialised to quadratic optimisation, we generalise known results by providing
a very simple bound for the convergence rate.
