A Distributed Algorithm for Convex Constrained Optimization Under Noise - Chatzipanagiotis, Nikolaos; Zavlanos, Michael M. (IEEE transactions on automatic control, 2016)
We present a novel distributed algorithm for convex constrained optimization problems that are subject to noise corruption and uncertainties. The proposed scheme can be classified as a distributed stochastic approximation method, where a unique feature here is that we allow for multiple noise terms to appear in both the computation and communication stages of the distributed iterative process. Specifically, we consider problems that involve multiple agents optimizing a separable convex objective function subject to convex local constraints and linear coupling constraints. This is a richer class of problems compared to those that can be handled by existing distributed stochastic approximation methods which consider only consensus constraints and fewer sources of noise. The proposed algorithm utilizes the augmented Lagrangian (AL) framework, which has been widely used recently to solve deterministic optimization problems in a distributed way. We show that the proposed method generates sequences of primal and dual variables that converge to their respective optimal sets almost surely.