  In this paper, we propose an algorithmic framework dubbed inertial
alternating direction methods of multipliers (iADMM), for solving a class of
nonconvex nonsmooth multiblock composite optimization problems with linear
constraints. Our framework employs the general minimization-majorization (MM)
principle to update each block of variables so as to not only unify the
convergence analysis of previous ADMM that use specific surrogate functions in
the MM step, but also lead to new efficient ADMM schemes. To the best of our
knowledge, in the \emph{nonconvex nonsmooth} setting, ADMM used in combination
with the MM principle to update each block of variables, and ADMM combined with
inertial terms for the primal variables have not been studied in the
literature. Under standard assumptions, we prove the subsequential convergence
and global convergence for the generated sequence of iterates. We illustrate
the effectiveness of iADMM on a class of nonconvex low-rank representation
problems.
