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 \(\mathcal{{O}}(1/k)\) in a convex setting and \(\mathcal{{O}}(1/k^2)\) 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.

建立了不精确的乘积交替交替方向方法（I-ADMM）的收敛速度，用于具有线性约束的一般可分离凸优化。遍历遍历和非遍历遍历都被分析。相对于迭代次数k，在凸设置下，收敛速度为\（\ mathcal {{O}}（1 / k）\），而\（\ mathcal {{O}}（1 / k ^ 2）\）在强凸的环境中。当误差边界条件成立时，该算法为两步线性收敛。在I-ADMM被设计成不精确迭代的准确性保留的全局收敛速度精确的迭代，从而导致测试问题，更好的数值性能。