The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large scale separable optimization problems, both for convex objective functions and for nonconvex objective functions. While there are a lot of convergence analysis for the convex case, the nonconvex case is still an open problem and the research for this case is in its infancy. In this talk, we consider two classes of optimization problems involving nonconvex functions. The first case is the “strongly+weakly” convex model and the second on is the general nonconvex model. For both cases, by using different analysis techniques, we prove the global convergence of the algorithms, and under some further conditions on the problem’s data, we also analyze the convergence rate.