# Convergence Rate Analysis of Proximal Iteratively Reweighted ℓ1 Methods for ℓp Regularization Problems

arXiv: https://arxiv.org/abs/2007.05747 · HTML: https://mlsanity.com/paper/2007.05747/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Avoiding strict saddle points of nonconvex regularized problems](https://mlsanity.com/paper/2401.09274/) (2024)
- [Alternating Iteratively Reweighted ℓ1 and Subspace Newton Algorithms for Nonconvex Sparse Optimization](https://mlsanity.com/paper/2407.17216/) (2024)

## Abstract (arXiv)

In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted ℓ1 algorithms for solving ℓp 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 ℓ1 algorithms.