The distributed alternating direction method of multipliers (ADMM) is one of the most widely used algorithms to solve large-scale optimization problems. Since the memory consumption, communication cost and convergence of the distributed ADMM are affected by the number of workers, how to improve the scalability of the distributed ADMM is one of the main challenges. To address this challenge, this paper proposes an asynchronous distributed ADMM based on the hybrid parallel model (HPAD-ADMM), which uses OpenMP for parallelization inside the node and MPI for message passing between nodes in the distributed system. Each worker solves sub-problem in parallel by multithreading, which reduces the system time at each iteration without affecting the convergence of the system or increasing the communication cost and memory consumption. Furthermore, this paper designs efficient parallelized algorithms to solve sub-problems for different applications. For the L1-regularized logistic regression problem, the sub-problem is solved by parallel trust region newton method and system time is reduced by adjusting the accuracy of the sub-problem. For the lasso problem, parallel matrix inversion algorithms are selected dynamically to reduce the system time according to the size of the data set. Finally, large-scale data sets are used to test the performance of the HPAD-ADMM. Experimental results show that compared with the state-of-the-art distributed ADMM, the HPAD-ADMM has higher scalability without losing accuracy.

乘法器的分布式交替方向法（ADMM）是解决大规模优化问题的最广泛使用的算法之一。由于分布式ADMM的内存消耗、通信成本和收敛性受到worker数量的影响，如何提高分布式ADMM的可扩展性是主要挑战之一。为了应对这一挑战，本文提出了一种基于混合并行模型（HPAD-ADMM）的异步分布式 ADMM，它使用 OpenMP 进行节点内部的并行化，并使用 MPI 进行分布式系统中节点之间的消息传递。每个worker通过多线程并行解决子问题，减少了系统每次迭代的时间，不影响系统的收敛性，也不会增加通信成本和内存消耗。此外，本文设计了高效的并行化算法来解决不同应用的子问题。对于L1正则化逻辑回归问题，子问题采用并行置信域牛顿法求解，通过调整子问题的精度来减少系统时间。对于套索问题，根据数据集的大小动态选择并行矩阵求逆算法以减少系统时间。最后，使用大规模数据集来测试 HPAD-ADMM 的性能。实验结果表明，与最先进的分布式 ADMM 相比，HPAD-ADMM 在不损失准确性的情况下具有更高的可扩展性。子问题采用并行置信域牛顿法求解，通过调整子问题的精度减少系统时间。对于套索问题，根据数据集的大小动态选择并行矩阵求逆算法以减少系统时间。最后，使用大规模数据集来测试 HPAD-ADMM 的性能。实验结果表明，与最先进的分布式 ADMM 相比，HPAD-ADMM 在不损失准确性的情况下具有更高的可扩展性。子问题采用并行置信域牛顿法求解，通过调整子问题的精度减少系统时间。对于套索问题，根据数据集的大小动态选择并行矩阵求逆算法以减少系统时间。最后，使用大规模数据集来测试 HPAD-ADMM 的性能。实验结果表明，与最先进的分布式 ADMM 相比，HPAD-ADMM 在不损失准确性的情况下具有更高的可扩展性。