A Sequential Complete Inertial Bregman Admm for Multi-Block Nonconvex Problems

In this paper, a sequential complete inertial Bregman alternating direction method of multipliers (SCIB-ADMM) is proposed for multi-block nonconvex problems. The iterative method is established by utilizing the inertial strategy and Bregman distance to enhance its processing speed and efficiency. At each iteration, the SCIB-ADMM method utilizes two different relaxation factors and updates the Lagrange multiplier twice. The convergence of the SCIB-ADMM can be established under appropriate assumptions. Moreover, numerical experiments are presented on smoothly clipped absolute deviation (SCAD) and robust principal component analysis (PCA) problems to show the effectiveness of the SCIB-ADMM method.