标题： 一种用于非Lipschitz组稀疏优化的快速迭代阈值和支撑与尺度收缩算法（fits3）（i）：最小二乘保真度的情况 显示英文标题

标题： A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity

摘要： 我们考虑设计一种新的高效且易于实现的算法，以解决具有非凸非Lipschitz正则化的通用组稀疏优化模型，称为快速迭代阈值和支撑-尺度收缩算法（FITS3）。 在本文中，我们关注最小二乘保真度的情况。 FITS3 是从这类模型的下界理论出发，并结合阈值操作、线性化和外推技术设计的。 FITS3 具有两个优势。 首先，它非常高效，特别适用于大规模问题，因为它采用支撑-尺度收缩，不需要求解任何线性或非线性系统。 对于两个重要的特殊情况，FITS3 仅包含如矩阵-向量乘法和软阈值等简单的计算。 其次，在适当假设下，FITS3 算法具有序列收敛性保证。 数值实验和与最近存在的非Lipschitz组恢复算法的比较表明，所提出的 FITS3 能达到类似的恢复精度，但相比第二快的算法，对于中等或大规模问题，其 CPU 时间仅需大约一半。 显示英文摘要

摘要： We consider to design a new efficient and easy-to-implement algorithm to solve a general group sparse optimization model with a class of non-convex non-Lipschitz regularizations, named as fast iterative thresholding and support-and-scale shrinking algorithm (FITS3). In this paper we focus on the case of a least-squares fidelity. FITS3 is designed from a lower bound theory of such models and by integrating thresholding operation, linearization and extrapolation techniques. The FITS3 has two advantages. Firstly, it is quite efficient and especially suitable for large-scale problems, because it adopts support-and-scale shrinking and does not need to solve any linear or nonlinear system. For two important special cases, the FITS3 contains only simple calculations like matrix-vector multiplication and soft thresholding. Secondly, the FITS3 algorithm has a sequence convergence guarantee under proper assumptions. The numerical experiments and comparisons to recent existing non-Lipschitz group recovery algorithms demonstrate that, the proposed FITS3 achieves similar recovery accuracies, but costs only around a half of the CPU time by the second fastest compared algorithm for median or large-scale problems.