In this paper, we analyze the behavior of the alternating direction method of multipliers (ADMM), for solving a family of nonconvex problems. Our focus is given to the well-known consensus and shar ing problems, both of which have wide applications in signal pro cessing. We show that in the presence of nonconvex objective func tion, classical ADMM is able to reach the set of stationary solutions for these problems, if the stepsize is chosen large enough. An inter esting consequence of our analysis is that the ADMM is convergent for a family of sharing problems, regardless of the number of block s or the convexity of the objective function. Our analysis is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules.
In REF , Hong et al. analyzed the convergence of the ADMM for solving certain nonconvex consensus and sharing problems.
Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Computer Science Mathematics