Distributed Asynchronous Random Projection Algorithm (DARPA) with Arbitrary Uniformly Bounded Delay

In this paper, an asynchronous random projection algorithm is introduced to solve a distributed constrained convex optimization problem over a time-varying multi-agent network. In this asynchronous case, each agent computes its estimate by exchanging information with its neighbors within a bounded delay lapse. For diminishing uncoordinated stepsizes and some standard conditions on the gradient errors, we provide a convergence analysis of Distributed Asynchronous Random Projection Algorithm (DARPA) to the same optimal point under an arbitrary uniformly bounded delay.