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 algorithms for solving 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 algorithms.
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}
}