Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem - Yang Liu; Yazheng Dang (Journal of Mathematics)
The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the convergence under some suitable conditions. Simulation experiment verifies the effectiveness and feasibility of the proposed method.