Distributed Consensus Optimization with Consensus ALADIN

Abstract: TThe paper proposes the Consensus Augmented Lagrange Alternating Direction Inexact Newton (Consensus ALADIN) algorithm, a novel approach for solving distributed consensus optimization problems (DC). Consensus ALADIN allows each agent to independently solve its own nonlinear programming problem while coordinating with other agents by solving a consensus quadratic programming (QP) problem. Building on this, we propose Broyden-Fletcher-Goldfarb-Shanno (BFGS) Consensus ALADIN, a communication-and-computation-efficient Consensus ALADIN.BFGS Consensus ALADIN improves communication efficiency through BFGS approximation techniques and enhances computational efficiency by deriving a closed form for the consensus QP problem. Additionally, by replacing the BFGS approximation with a scaled identity matrix, we develop Reduced Consensus ALADIN, a more computationally efficient variant. We establish the convergence theory for Consensus ALADIN and demonstrate its effectiveness through application to a non-convex sensor allocation problem.