Geometrical Convergence Rate for Distributed Optimization with Time-Varying Directed Graphs and Uncoordinated Step-Sizes

Understand

This paper studies a class of distributed optimization algorithms by a set of agents, where each agent has only access to its own local convex objective function, and jointly minimizes the sum of the 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 also exactly steers all the agents to asymptotically converge to a global and consensual optimal solution even under the assumption that the step-sizes are uncoordinated.
• Two fairly standard conditions for achieving the geometrical convergence rate are established under the assumption that the objective functions are strong convexity and have Lipschitz continuous gradient.