  The Sibson and Arimoto capacity, which are based on the Sibson and Arimoto
mutual information (MI) of order {\alpha}, respectively, are well-known
generalizations of the channel capacity C. In this study, we derive novel
alternating optimization algorithms for computing these capacities by providing
new variational characterizations of the Sibson and Arimoto MI. Moreover, we
prove that all iterative algorithms for computing these capacities are
equivalent under appropriate conditions imposed on their initial distributions.
