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.