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

TL;DR

This paper introduces FITS3, an efficient iterative algorithm for non-convex, non-Lipschitz group sparse optimization with least-squares fidelity, offering fast performance and convergence guarantees for large-scale problems.

Contribution

FITS3 is a novel, simple, and efficient algorithm that avoids solving complex systems and is specifically designed for large-scale non-Lipschitz group sparse problems.

Findings

FITS3 achieves similar recovery accuracy as existing algorithms.

FITS3 reduces CPU time by about half compared to the second fastest method.

FITS3 is suitable for large-scale problems due to support-and-scale shrinking.

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.