Multi-leader multi-follower game-based ADMM for big data processing

Alternating direction method of multipliers (ADMM) is a promising approach to solve “big data” problems due to its efficient variable decomposition and fast convergence. However, it is subject to the following two fundamental assumptions: no contradiction among multiple controllers' objectives and ideal feedback from the agents to the controllers. In this paper, a multiple-leader multiple-follower (MLMF) game-based ADMM is developed to balance the conflicting objectives among the controllers as well as those between the controllers and the agents. Both analytical and simulation results verify that the proposed method reaches a hierarchical social optimum and converges at a linear speed. More importantly, the convergence rate is independent of the network size, which indicates that the MLMF game-based ADMM can be used in a very large network for big data processing.