English

Convergence Rate Analysis of Proximal Iteratively Reweighted $\ell_1$ Methods for $\ell_p$ Regularization Problems

Optimization and Control 2021-01-12 v2

Abstract

In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted 1\ell_1 algorithms for solving p\ell_p regularization problems, which are widely applied for inducing sparse solutions. We show that if the Kurdyka-Lojasiewicz (KL) property is satisfied, the algorithm converges to a unique first-order stationary point; furthermore, the algorithm has local linear convergence or local sublinear convergence. The theoretical results we derived are much stronger than the existing results for iteratively reweighted 1\ell_1 algorithms.

Keywords

Cite

@article{arxiv.2007.05747,
  title  = {Convergence Rate Analysis of Proximal Iteratively Reweighted $\ell_1$ Methods for $\ell_p$ Regularization Problems},
  author = {Hao Wang and Hao Zeng and Jiashan Wang},
  journal= {arXiv preprint arXiv:2007.05747},
  year   = {2021}
}
R2 v1 2026-06-23T17:02:28.582Z