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

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.