论文标题
适用于可分离凸优化的不精确ADMM的收敛速率
Convergence rates for an inexact ADMM applied to separable convex optimization
论文作者
论文摘要
对于不精确加速的交替方向方法，建立了收敛速率（I-ADMM），用于使用线性约束的一般可分离凸优化。分析了沿阵行和非共性迭代。相对于迭代编号K，在凸设置中的收敛速率为O（1/K），在强凸设置中为O（1/K^2）。当误差结合条件保持时，该算法是2步线性收敛。 I-ADMM的设计使得不精确迭代的准确性保留了精确迭代的全局收敛速率，从而在测试问题中提供了更好的数值性能。
Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed. Relative to the iteration number k, the convergence rate is O(1/k) in a convex setting and O(1/k^2) in a strongly convex setting. When an error bound condition holds, the algorithm is 2-step linearly convergent. The I-ADMM is designed so that the accuracy of the inexact iteration preserves the global convergence rates of the exact iteration, leading to better numerical performance in the test problems.
