Global convergence of proximal iteratively reweighted algorithm

In this paper, we investigate the convergence of the proximal iteratively reweighted algorithm for a class of nonconvex and nonsmooth problems. Such problems actually include numerous models in the area of signal processing and machine learning research. Two extensions of the algorithm are also studied. We provide a unified scheme for these three algorithms. With the Kurdyka–Łojasiewicz property, we prove that the unified algorithm globally converges to a critical point of the objective function.