Convergence rate analysis of proximal iteratively reweighted ℓ _1 methods for ℓ _p regularization problems

In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted ℓ _1 algorithms for solving ℓ _p regularization problems, which are widely applied for inducing sparse solutions. We show that if the Kurdyka–Łojasiewicz 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 ℓ _1 algorithms.