The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit sparsity in the problem data, it is particularly suitable for large-scale optimization. However, the method may still take prohibitively long to compute solutions to very large problem instances. Although ADMM is known to be parallelizable, this feature is rarely exploited in real implementations. In this paper we exploit the parallel computing architecture of a graphics processing unit (GPU) to accelerate ADMM. We build our solver on top of OSQP, a state-of-the-art implementation of ADMM for quadratic programming. Our open-source CUDA C implementation has been tested on many large-scale problems and was shown to be up to two orders of magnitude faster than the CPU implementation.

乘数交替方向法（ADMM）是解决结构化凸优化问题的强大算子拆分技术。由于其每次迭代的计算成本相对较低，并且能够利用问题数据中的稀疏性，因此特别适合大规模优化。但是，该方法可能仍需要花费很长的时间才能计算出非常大的问题实例的解决方案。尽管已知ADMM可并行化，但在实际实现中很少利用此功能。在本文中，我们利用图形处理单元（GPU）的并行计算体系结构来加速ADMM。我们在OSQP之上构建求解器，OSQP是用于二次编程的ADMM的最新实现。