Random Gradient-Free Optimization for Multiagent Systems With Communication Noises Under a Time-Varying Weight Balanced Digraph

In this paper, we focus on a constrained convex optimization problem of multiagent systems under a time-varying topology. In such topology, it is not only B-strongly connected, but the communication noises are also existent. Each agent has access to its local cost function, which is a nonsmooth function. A gradient-free random protocol is come up with minimizing a sum of cost functions of all agents, which are projected to local constraint sets. First, considering the stochastic disturbances in the communication channels among agents, the upper bounds of disagreement estimate of agents' states are obtained. Second, a sufficient condition on choosing step sizes and smoothing parameters is derived to guarantee that all agents almost surely converge to the stationary optimal point. At last, a numerical example and a comparison are provided to illustrate the feasibility of the random gradient-free algorithm.