Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem
Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem
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DOI：
10.4208/eajam.270812.161112a
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发表时间：
2012-11
影响因子：
1.2
通讯作者：
R. Chan;M. Tao;Xiaoming Yuan
中科院分区：
文献类型：
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作者：
R. Chan;M. Tao;Xiaoming Yuan
乘子交替方向法（ADMM）被应用于一个有约束的线性最小二乘问题，其中目标函数是两个最小二乘项之和，并且存在箱约束。在每次迭代中，原始问题被分解为两个更简单的最小二乘子问题，并且为了加速内部迭代，每当相关子问题没有已知的闭式解时，我们将其线性化。我们证明了所得算法的收敛性，并将其应用于解决一些图像去模糊问题。与牛顿型方法相比，其效率得到了证明。
The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.