The Augustin--Csisz{\' a}r mutual information (MI) and Lapidoth--Pfister MI are well-known generalizations of the Shannon MI, but do not have known closed-form expressions, so they need to be calculated by solving optimization problems. In this study, we propose alternating optimization algorithms for computing these types of MI and present proofs of their global convergence properties. We also provide a novel variational characterization of the Augustin--Csisz{\' a}r MI that is similar to that of the Sibson MI.

翻译：Augustin-Csiszár互信息(MI)与Lapidoth-Pfister互信息是香农互信息的著名推广形式，但尚无已知的闭式表达式，需通过求解优化问题进行计算。本研究提出用于计算这两类互信息的交替优化算法，并给出其全局收敛性证明。我们还给出了Augustin-Csiszár互信息的一种新型变分刻画，该刻画与Sibson互信息的变分形式相似。