A Generic Algorithm Framework for Distributed Optimization Over the Time-Varying Network With Communication Delays

In this article, we study the distributed optimization problem (DOP) over the time-varying communication network topology with communication delays. The existing distributed optimization algorithms (DOAs) cannot be directly applied to DOPs over the time-varying network with communication delays. In this article, by adding new virtual agents and redefining communication links, some delay properties are realized and existing DOAs can then be reused to solve the DOPs. Thus, a generic algorithm framework is established, which can apply to many important DOAs, such as the mirror descent algorithm and dual averaging algorithm, to solve DOPs over the time-varying network with communication delays. The convergence results of the DOAs are established and verified under the generic algorithm framework.