Inexact alternating direction methods of multipliers for separable convex optimization
Inexact alternating direction methods of multipliers for separable convex optimization
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DOI：
10.1007/s10589-019-00072-2
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发表时间：
2019-02
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
本文提出了一种非精确交替方向乘子法（ADMMs），用于求解一般的可分凸优化问题，其目标函数为光滑项和非光滑项之和，且带有线性约束.该方法涉及线性化的子问题，回代步骤，梯度或加速梯度技术。建立了全局收敛。当ADMM子问题没有封闭形式解或子问题的解是昂贵的时，该方法特别有用。基于图像重建问题的数值实验表明了所提方法的有效性。
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.