Alternating Optimization Approach for Computing $\alpha$-Mutual Information and $\alpha$-Capacity

This study presents alternating optimization (AO) algorithms for computing $\alpha$-mutual information ($\alpha$-MI) and $\alpha$-capacity based on variational characterizations of $\alpha$-MI using a reverse channel. Specifically, we derive several variational characterizations of Sibson, Arimoto, Augustin--Csisz{\' a}r, and Lapidoth--Pfister MI and introduce novel AO algorithms for computing $\alpha$-MI and $\alpha$-capacity; their performances for computing $\alpha$-capacity are also compared. The comparison results show that the AO algorithm based on the Sibson MI's characterization has the fastest convergence speed.