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Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
S. S. Kia, J. Cortés, S. Martínez
Automatica 55 (2015), 254-264

Abstract

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is strictly convex and equal to a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. We also characterize the algorithm's privacy preservation properties and its correctness under time-varying interaction topologies. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We consider three scenarios: periodic, centralized event-triggered, and distributed event-triggered communication. First, we provide an upper bound on the stepsize that guarantees exponential convergence over connected undirected graphs for implementations with periodic communication. Building on this result, we design a provably correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.

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