非精确ADMM用于可分凸优化的收敛速度
Convergence rates for an inexact ADMM applied to separable convex optimization
摘要：
研究了一般可分线性约束凸优化的不精确加速交替方向乘子法（I-ADMM）的收敛速度.遍历和非遍历迭代进行了分析。相对于迭代次数k，在凸情形下的收敛速度为O（1/k），在强凸情形下的收敛速度为O（1/k^2）.当误差界条件成立时，算法是两步线性收敛的。I-ADMM的设计使得不精确迭代的精度保持精确迭代的整体收敛速度，从而在测试问题中获得更好的数值性能。
英文摘要：
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.
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