Alternating direction method of multipliers for nonconvex fused regression problems
Alternating direction method of multipliers for nonconvex fused regression problems
复制标题
非凸融合回归问题的乘子交替方向法
DOI：
10.1016/j.csda.2019.01.002
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
Kong Lingchen
中科院分区：
文献类型：
--
作者：
Xiu Xianchao;Liu Wanquan;Li Ling;Kong Lingchen
众所周知，融合最小绝对收缩和选择算子(FLASSO)在信号和图像处理中发挥着重要作用。近年来，非凸罚因其在稀疏学习中的成功而被广泛研究。本文提出了一种新的非凸融合回归模型，该模型将FLASSO算法和非凸罚函数有机地结合在一起。由于每个导出子问题都有一个闭合形式的解，改进的交替方向乘子法(ADMM)被证明是非常有效的。此外，还从数学上讨论并证明了该算法的收敛特性。这导致了一个快速且收敛的算法。大量的数值实验表明，我们提出的非凸融合回归方法比最先进的FLASSO方法具有更好的性能。
It is well-known that the fused least absolute shrinkage and selection operator (FLASSO) has been playing an important role in signal and image processing. Recently, the nonconvex penalty is extensively investigated due to its success in sparse learning. In this paper, a novel nonconvex fused regression model, which integrates FLASSO and the nonconvex penalty nicely, is proposed. The developed alternating direction method of multipliers (ADMM) approach is shown to be very efficient owing to the fact that each derived subproblem has a closed-form solution. In addition, the convergence is discussed and proved mathematically. This leads to a fast and convergent algorithm. Extensive numerical experiments show that our proposed nonconvex fused regression outperforms the state-of-the-art approach FLASSO.