论文标题
无基质操作的一阶数值算法
A First-Order Numerical Algorithm without Matrix Operations
论文作者
论文摘要
本文提供了一种无基质的一阶数值方法来解决大规模的圆锥优化问题。线性方程的求解系统在一阶数值和二阶数值算法中构成了最具挑战性的部分。现有的直接和间接方法在计算上是昂贵的，要么在解决方案准确性上妥协。另外，我们提出了一种易于计算的分解方法，以解决在圆锥优化问题中出现的稀疏线性系统。它的迭代具有易于处理的，高度可行的，具有封闭式溶液。该算法可以在分布式平台（例如图形处理单元）上轻松实现，并具有量度的时间改进。在大规模的圆锥优化问题上证明了所提出的求解器的性能，并与最先进的一阶求解器进行了比较。
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical algorithms. Existing direct and indirect methods are either computationally expensive or compromise on solution accuracy. Alternatively, we propose an easy-to-compute decomposition method to solve sparse linear systems that arise in conic optimization problems. Its iterations are tractable, highly parallelizable, with closed-form solutions. This algorithm can be easily implemented on distributed platforms, such as graphics processing units, with orders-of-magnitude time improvement. The performance of the proposed solver is demonstrated on large-scale conic optimization problems and is compared with the state-of-the-art first-order solvers.
