Distributed asynchronous time-varying constrained optimization

We devise a distributed asynchronous gradient-based algorithm to enable a network of computing and communicating nodes to solve a constrained discrete-time time-varying convex optimization problem. Each node updates its own decision variable only once every discrete time step. Under some assumptions (strong convexity, Lipschitz continuity of the gradient, persistent excitation), we prove the algorithm's asymptotic convergence in expectation to an error bound whose size is related to the constant stepsize choice and the variability in time of the optimization problem. Moreover, the convergence rate is linear. In addition, we present an interesting by-product of the proposed algorithm in the context of time-varying consensus, and we discuss some numerical evaluations in multi-robot scenarios to assess the algorithm performance and the tightness of the proven asymptotic bounds.