Iterative minimization algorithms appear in various areas including machine learning, neural network, and information theory. The em algorithm is one of the famous one in the former area, and Arimoto-Blahut algorithm is a typical one in the latter area. However, these two topics had been separately studied for a long time. In this paper, we generalize an algorithm that was recently proposed in the context of Arimoto-Blahut algorithm. Then, we show various convergence theorems, one of which covers the case when each iterative step is done approximately. Also, we apply this algorithm to the target problem in em algorithm, and propose its improvement. In addition, we apply it to other various problems in information theory.

翻译：迭代最小化算法出现在包括机器学习、神经网络和信息理论在内的多个领域。EM算法是前一个领域中的著名算法之一，而Arimoto-Blahut算法则是后一个领域中的典型代表。然而，长期以来这两个主题一直被分开研究。在本文中，我们推广了一种最近在Arimoto-Blahut算法背景下提出的算法。随后，我们展示了多种收敛定理，其中一种定理涵盖了每次迭代步骤近似完成的情况。此外，我们将该算法应用于EM算法中的目标问题，并提出了其改进方案。同时，我们还将该算法应用于信息理论中的其他各种问题。