A Totally Asynchronous Algorithm for Time-Varying Convex Optimization Problems

Abstract

This paper presents a decentralized algorithm for a team of agents to track time-varying fixed points that are the solutions to time-varying convex optimization problems. The algorithm is first-order, and it allows for total asynchrony, i.e., all communications and computations can occur with arbitrary timing and arbitrary (finite) delays. Convergence rates are computed in terms of the communications and computations that agents execute, without specifying when they must occur. These rates apply to convergence to the minimum of each individual objective function, as well as agents’ long-run behavior as their objective functions change. Then, to improve the usage of limited communication and computation resources, we optimize the timing of agents’ operations relative to changes in their objective functions to minimize fixed point tracking error over time. Simulation results illustrate these developments.