Multi-block relaxed-dual linear inertial ADMM algorithm for nonconvex and nonsmooth problems with nonseparable structures

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.