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

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