A Symmetric Alternating Direction Method of Multipliers for Separable Nonconvex Minimization Problems

In this paper, we propose a symmetric alternating method of multipliers for minimizing the sum of two nonconvex functions with linear constraints, which contains the classic alternating direction method of multipliers in the algorithm framework. Based on the powerful Kurdyka-Łojasiewicz property, and under some assumptions about the penalty parameter and objective function, we prove that each bounded sequence generated by the proposed method globally converges to a critical point of the augmented Lagrangian function associated with the given problem. Moreover, we report some preliminary numerical results on solving l1/2 regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.