Geometrical convergence rate for distributed optimization with time-varying directed graphs and uncoordinated step-sizes

摘要

Highlights?The communications among agents are described by a sequence of time-varying directed graphs which are assumed to be uniformly strongly connected.?Two standard conditions for achieving the geometrical convergence rate are established.?The theoretical analysis shows that the distributed algorithm is capable of driving the whole network to geometrically converge to an optimal solution.AbstractThis paper studies a class of distributed optimization algorithms by a set of agents, where each agent only has access to its own local convex objective function, and the goal of the agents is to jointly minimize the sum of all the local functions. The communications among agents are described by a sequence of time-varying directed graphs which are assumed to be uniformly strongly connected. A column stochastic mixing matrices is employed in the algorithm which exactly steers all the agents to asymptotically converge to a global and consensual optimal solution even under