Blended dynamics approach to distributed optimization: Sum convexity and convergence rate

Abstract

© 2022 Elsevier LtdIn this paper, we introduce the concept of the blended dynamics of the multi-agent system, which is constructed using dynamics of individual agents. The blended dynamics approach is applied to the distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need not be convex as long as the global cost function is strongly convex and (ii) the convergence rate of the distributed algorithm is arbitrarily close to the convergence rate of the centralized one. Two particular continuous-time algorithms are presented using the proportional–integral-type couplings. One has benefit of initialization-free, so that agents can join or leave the network during the operation. The other one has the minimal amount of communication information. After presenting a general theorem that can be used for designing distributed algorithms, we particularly present a distributed heavy-ball method and discuss its strength over other methods.