  This paper proves the convergence of Bayes-optimal orthogonal/vector
approximate message-passing (AMP) to a fixed point in the large system limit.
The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that
is guaranteed to converge systematically. The dynamics of Bayes-optimal LM-MP
is analyzed via an existing state evolution framework. The obtained state
evolution recursions are proved to converge. The convergence of Bayes-optimal
orthogonal/vector AMP is proved by confirming an exact reduction of the state
evolution recursions to those for Bayes-optimal orthogonal/vector AMP.
