Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval (0,2). To the best of our knowledge, all related papers in the literature only consider the case where the over-relaxation parameter lies in the interval (0,(1+√5)/2).