Convergence rate analysis of proximal iteratively reweighted l₁ 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 KurdykaLojasiewicz 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.