An inertial proximal partially symmetric ADMM-based algorithm for linearly constrained multi-block nonconvex optimization problems with applications

The alternating direction method of multipliers (ADMM) is an efficient splitting method for solving separable optimization with linear constraints. In this paper, an inertial proximal partially symmetric ADMM is proposed for solving linearly constrained multi-block nonconvex separable optimization, which can improve the computational efficiency by considering the ideas of inertial proximal point and linearization technique. Meanwhile, the proposed method updates the Lagrange multiplier twice and considers different relaxation factors in each iteration. Under the assumption that the generated sequence is bounded and the auxiliary function satisfies the Kurdyka-Łojasiewicz property, the global convergence of the proposed method with a more relaxed parameter range is analyzed. Moreover, some numerical results on SCAD (for smoothly clipped absolute deviation), image processing and robust PCA nonconvex problems are reported to demonstrate the efficiency and superiority of the proposed method.