Distributed Augmentation-Regularization for Robust Online Convex Optimization

Abstract This paper studies the use of distributed, primal-dual dynamics to solve continuous, time-dependent optimization problems on the fly. When using primal-dual dynamics, the availability of a strongly convex-strongly concave Lagrangian is desirable, but this is a strong assumption not satisfied in many applications. To deal with this, we develop a new Lagrangian regularization technique that seeks to minimize the perturbation to the original solutions and is compatible with the distributed nature of the optimization problem. We provide analytic bounds of the tracking error of the optimal solution using standard Lyapunov stability analysis techniques. As an application, we consider a receding horizon formulation of a dynamic traffic assignment problem and illustrate the performance of our approach in simulation.