A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity
Abstract
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.
Cite
@article{arxiv.2501.04491,
title = {A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity},
author = {Yanan Zhao and Qiaoli Dong and Yufei Zhao and Chunlin Wu},
journal= {arXiv preprint arXiv:2501.04491},
year = {2025}
}