A Framework of Inertial Regularized ADMM for Separable Nonconvex Optimization Problems

Abstract The alternating direction method of multipliers (ADMM) is an effective algorithm for solving optimization problems with separable structures. Recently, inertial technique has been widely used in various algorithms to accelerate its convergence speed and enhance the numerical performance. There are a lot of convergence analyses for solving the convex optimization problems by combining inertial technique with ADMM, while the research on the nonconvex cases is still in its infancy. In this paper, we propose an algorithm framework of inertial regularized ADMM (iRADMM) for a class of two-block nonconvex optimization problems. Under some assumptions, we establish the global and strong convergence of the proposed method. Furthermore, we apply the iRADMM to solve the signal recovery, image reconstruction and SCAD penalty problem. The numerical results demonstrate the efficiency of the iRADMM algorithm and also illustrate the effectiveness of the introduced inertial term.