  In this paper, we propose an inertial alternating direction method of
multipliers for solving a class of non-convex multi-block optimization problems
with \emph{nonlinear coupling constraints}. Distinctive features of our
proposed method, when compared with other alternating direction methods of
multipliers for solving non-convex problems with nonlinear coupling
constraints, include: (i) we apply the inertial technique to the update of
primal variables and (ii) we apply a non-standard update rule for the
multiplier by scaling the multiplier by a factor before moving along the ascent
direction where a relaxation parameter is allowed. Subsequential convergence
and global convergence are presented for the proposed algorithm.
