A Robust Block-Jacobi Algorithm for Quadratic Programming under Lossy Communications

We address the problem distributed quadratic programming under lossy communications where the global cost function is the sum of coupled local cost functions, typical in localization problems and partition-based state estimation. We propose a novel solution based on a generalized gradient descent strategy, namely a Block-Jacobi descent algorithm, which is amenable for a distributed implementation and which is provably robust to communication failure if the step size is sufficiently small. Interestingly, robustness to packet loss, implies also robustness of the algorithm to broadcast communication protocols, asynchronous computation and bounded random communication delays. The theoretical analysis relies on the separation of time scales and singular perturbation theory. Our algorithm is numerically studied in the context of partition-based state estimation in smart grids based on the IEEE 123 nodes distribution feeder benchmark. The proposed algorithm is observed to exhibit a similar convergence rate when compared with the well known ADMM algorithm with no packet losses, while it has considerably better performance when including moderate packet losses.