Distributed quantized random gradient-free algorithm with event triggered communication

We study the distributed constraint optimization problem of multi-agent systems, where each agent only knows its own local objective function and a global non-empty constraint set and the optimal solution of the optimization problem is finally obtained by communicating with neighbor nodes. The proposed algorithm is for the case that the communication network is time-varying unbalanced digraphs and each agent does not know its out-degree. Considering the limited bandwidth and communication cost in reality, the quantization technology based on coding and decoding scheme is used to preprocess the communication information between nodes and the event triggered broadcasting technology is also used to reduce the communication times of the networks. Gaussian smooth function and gradient-free oracle are introduced to replace the traditional subgradient method in this paper. We propose a distributed quantized random gradient-free algorithm based on event triggering communication, and under the condition that the objective function is convex and Lipschitz continuous, it is proved that the proposed algorithm can converge to the neighborhood of the optimal value. Furthermore, the update rule of quantization level that makes the quantizer unsaturated is given. Finally, numerical simulations are provided to illustrate the validity and feasibility of the algorithm. © 2021, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.