论文标题
排名两次的平行分裂版本的增强拉格朗日方法，其步长为（0,2），用于可分离的凸编程
A rank-two relaxed parallel splitting version of the augmented Lagrangian method with step size in (0,2) for separable convex programming
论文作者
论文摘要
增强拉格朗日方法（ALM）对于具有线性约束的规范凸编程问题是经典的，并且在各种科学计算领域都发现了许多应用。 ALM的主要优点是，更新双重变量的步骤可以在$（0,2）$中进一步放松，并且此优势很容易导致ALM的数值加速度。当讨论可分离的凸编程问题并考虑经典ALM的相应拆分版本时，可以保证收敛性，因此，可以将$（0,2）$的步长以更新双重变量的放松步骤，似乎不可能进行$（0,2）$的步长。我们表明，对于ALM的平行分裂版本，如果放松步骤简单地通过等级两矩阵校正，则可以维持$（0,2）$的步长以进一步放松原始变量。因此，提出了可分离的凸面编程问题，提出了$（0,2）$的步长尺寸的RANC-TWO轻松平行分裂版本。我们验证新算法可以通过测试某些应用程序来显着胜过同类算法的现有算法。
The augmented Lagrangian method (ALM) is classic for canonical convex programming problems with linear constraints, and it finds many applications in various scientific computing areas. A major advantage of the ALM is that the step for updating the dual variable can be further relaxed with a step size in $(0,2)$, and this advantage can easily lead to numerical acceleration for the ALM. When a separable convex programming problem is discussed and a corresponding splitting version of the classic ALM is considered, convergence may not be guaranteed and thus it is seemingly impossible that a step size in $(0,2)$ can be carried on to the relaxation step for updating the dual variable. We show that for a parallel splitting version of the ALM, a step size in $(0,2)$ can be maintained for further relaxing both the primal and dual variables if the relaxation step is simply corrected by a rank-two matrix. Hence, a rank-two relaxed parallel splitting version of the ALM with a step size in $(0,2)$ is proposed for separable convex programming problems. We validate that the new algorithm can numerically outperform existing algorithms of the same kind significantly by testing some applications.
