Inertial alternating direction method of multipliers for non-convex non-smooth optimization

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