In this paper, we propose a multi-block relaxed-dual linear inertial alternating direction method of multipliers (MBRD-LIADMM) for solving the nonconvex and nonsmooth multi-block optimization problems with nonseparable structures, which combines the inertial technology, the relaxed-dual term and linear ADMM. The paper not only gives the simple condition to ensure the boundedness of the iterative sequence generated by the algorithm, but also proves the global convergence under the help of Kurdyka-Łojasiewicz property, which means that the generated sequence converges to a stationary point of the problem. Finally, two experiments are carried out to demonstrate the feasibility and effectiveness of the proposed algorithm.

本文提出了一种多块松弛对偶线性惯性交替方向乘子法（MBRD-LIADMM），用于求解不可分离结构的非凸非光滑多块优化问题，该方法结合了惯性技术、松弛对偶线性惯性交替方向法（MBRD-LIADMM）。项和线性 ADMM。论文不仅给出了保证算法生成的迭代序列有界性的简单条件，而且借助Kurdyka-Łojasiewicz性质证明了全局收敛性，即生成的序列收敛到问题的驻点。最后通过两个实验验证了所提算法的可行性和有效性。