Distributed Fast-Tracking Alternating Direction Method of Multipliers (ADMM) Algorithm with Optimal Convergence Rate
Shreyansh Shethia, Akshita Gupta, Omanshu Thapliyal, Inseok Hwang · 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC) · 2021
In this paper, we consider a distributed optimization problem with coupled constraints, where a network of agents aim to cooperatively minimize the sum of their local objective functions, subject to individual constraints. The primary goal is to improve the convergence rate of the existing Tracking Alternating Direction Method of Multipliers (TADMM) algorithm to solve the above distributed optimization problem. To this end, an upper bound on the convergence rate factor of the TADMM algorithm is derived in terms of the weight matrix of the network. To achieve faster convergence, the optimal weight matrix is computed using a semi-definite programming (SDP) formulation. Lastly, we implement the optimization problem in a Distributed Model-Predictive Control problem for a group of aircraft in formation flight and solve it using both Fast-Tracking ADMM (F-TADMM) and TADMM to demonstrate faster convergence of the proposed algorithm.