Accelerated bregman operator splitting with backtracking
Accelerated bregman operator splitting with backtracking
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DOI：
10.3934/ipi.2017048
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发表时间：
2017-09
影响因子：
1.3
通讯作者：
Yunmei Chen;Xianqi Li;Yuyuan Ouyang;E. Pasiliao
中科院分区：
文献类型：
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作者：
Yunmei Chen;Xianqi Li;Yuyuan Ouyang;E. Pasiliao
针对正则化大规模线性反问题，提出了两种带回溯的加速Bregman算子分裂（BOS）算法.第一种算法通过在可行集有界的假设下结合Nesterov的多步加速方案，在目标函数中的平滑分量方面提高了BOSVS [ 5 ]的收敛速度。第二个算法是能够处理的情况下，可行集是无界的。此外，它允许更积极的步长比在第一个计划，通过适当地选择惩罚参数和联合更新的加速参数和步长。这两种算法都表现出比BOSVS和AAMM更好的实际性能[ 21 ]，同时保持与AAMM相同的加速收敛速度。基于全变分的图像重建问题的数值结果表明了所提算法的有效性。
This paper develops two accelerated Bregman Operator Splitting (BOS) algorithms with backtracking for solving regularized large-scale linear inverse problems, where the regularization term may not be smooth. The first algorithm improves the rate of convergence for BOSVS [ 5 ] in terms of the smooth component in the objective function by incorporating Nesterov's multi-step acceleration scheme under the assumption that the feasible set is bounded. The second algorithm is capable of dealing with the case where the feasible set is unbounded. Moreover, it allows more aggressive stepsize than that in the first scheme by properly selecting the penalty parameter and jointly updating the acceleration parameter and stepsize. Both algorithms exhibit better practical performance than BOSVS and AADMM [ 21 ], while preserve the same accelerated rate of convergence as that for AADMM. The numerical results on total-variation based image reconstruction problems indicate the effectiveness of the proposed algorithms.