Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem

Abstract

The nonconvex and nonsmooth optimization problem has been attracting increasing attention in recent years in image processing and machine learning research. The algorithm-based reweighted step has been widely used in many applications. In this paper, we propose a new, extended version of the iterative convex majorization–minimization method (ICMM) for solving a nonconvex and nonsmooth minimization problem, which involves famous iterative reweighted methods. To prove the convergence of the proposed algorithm, we adopt the general unified framework based on the Kurdyka–Łojasiewicz inequality. Numerical experiments validate the effectiveness of the proposed algorithm compared to the existing methods.