In Part I of this paper, we proposed and analyzed a novel algorithmic framework, termed penalty dual decomposition (PDD), for the minimization of a nonconvex nonsmooth objective function, subject to difficult coupling constraints. Part II of this paper is devoted to evaluation of the proposed methods in the following three timely applications, ranging from communication networks to data analytics: i) the max-min rate fair multicast beamforming problem; ii) the sum-rate maximization problem in multi-antenna relay broadcast networks; and iii) the volume-min based structured matrix factorization problem. By exploiting the structure of the aforementioned problems, we show that effective algorithms for all these problems can be devised under the PDD framework. Unlike the state-of-the-art algorithms, the PDD-based algorithms are proven to achieve convergence to stationary solutions of the aforementioned nonconvex problems. Numerical results validate the efficacy of the proposed schemes.

中文翻译：

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非光滑非凸优化的惩罚对偶分解方法——第二部分：应用

在本文的第一部分，我们提出并分析了一种新的算法框架，称为惩罚对偶分解 (PDD)，用于最小化受困难耦合约束的非凸非光滑目标函数。本文的第二部分致力于在以下三个及时应用中评估所提出的方法，范围从通信网络到数据分析：i) 最大-最小速率公平组播波束成形问题；ii) 多天线中继广播网络中的和速率最大化问题；和 iii) 基于体积最小的结构化矩阵分解问题。通过利用上述问题的结构，我们表明可以在 PDD 框架下设计所有这些问题的有效算法。与最先进的算法不同，基于 PDD 的算法被证明可以收敛到上述非凸问题的平稳解。数值结果验证了所提出方案的有效性。