Convergence rates for an inexact ADMM applied to separable convex optimization
Convergence rates for an inexact ADMM applied to separable convex optimization
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DOI：
10.1007/s10589-020-00221-y
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发表时间：
2020-01
影响因子：
2.2
通讯作者：
W. Hager;Hongchao Zhang
中科院分区：
文献类型：
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作者：
W. Hager;Hongchao Zhang
研究了线性约束下一般可分凸优化问题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，收敛速度分别在凸和强凸情形下。当误差界条件成立时，算法是两步线性收敛的。I-ADMM的设计使得非精确迭代的精度保持精确迭代的全局收敛速度，从而在测试问题中获得更好的数值性能。
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 numberk, the convergence rate isin a convex setting andin 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 theexactiteration, leading to better numerical performance in the test problems.