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arXiv · 2007.05747

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

Hao Wang·Hao Zeng·Jiashan Wang
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Abstract

In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted $\ell_1$ algorithms for solving $\ell_p$ 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 $\ell_1$ algorithms.

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Hao Wang, Hao Zeng, Jiashan Wang. 2020-07-11. Convergence Rate Analysis of Proximal Iteratively Reweighted $\ell_1$ Methods for $\ell_p$ Regularization Problems. https://arxiv.org/abs/2007.05747

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