Surplus-Based ADMM for Distributed Constrained Optimization over Directed Graphs

This paper introduces a distributed parallel Alternating Direction Method of Multipliers (ADMM) algorithm for solving the distributed constrained optimization problem over directed graphs. To effectively handle the effect of asymmetric information communication on the convergence of the optimization algorithm, a surplus-based averaging consensus algorithm is integrated into the ADMM-based optimization algorithm. Unlike existing distributed ADMM algorithms over directed graphs that focus on the case with solely local constraints, the proposed algorithm can deal with both local constraints and coupling constraints. Under the assumption that the objective function is convex and the underlying graph is strongly connected, the convergence of the surplus-based ADMM to an optimal solution of the distributed constrained problem is proved. Finally, numerical simulations are conducted to validate the effectiveness of the proposed algorithm.