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 nonconvex nonsmooth setting, ADMM used in combination with the MM principle to update each block of variables, and ADMM combined with \emph{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.

翻译：在本文中,我们提出一个算法框架,称为惯性交替的乘数方向方法(iADMM),以解决有线性限制的非convex非moth多块复合优化问题。我们的框架采用一般最小化原则来更新每一组变量,以便不仅统一以前在MM步骤中使用特定代用功能的ADMM的趋同分析,而且导致新的高效的ADMM计划。根据我们的知识,在非convex非mooth环境中,ADMMM与MM原则相结合,对每一组变量进行了更新,而在文献中并未研究ADMMM与原始变量的\emph{内义术语相结合。在标准假设下,我们证明后继性趋同和全球趋同于生成的序列。我们举例说明了IADMMM在非conex低级代表问题的类别上的有效性。