Abstract: As the existing distributed subgradient optimization algorithms are mainly based on ideal assumptions:the network topology is balanced and the communication among the network is usually the exact information of a state variable of each agent. To relax these assumptions, a distributed subgradient optimization algorithm for switched networks was proposed based on limited quantized information communication. All information along each dynamical edge was quantified by a uniform quantizer with a limited quantization level before being sent in an unbalanced switching network, then the convergence of the multi-agent distributed quantized subgradient optimization algorithm was proved by using non-quadratic Lyapunov function method. Finally, the simulation examples were given to demonstrate the effectiveness of the proposed algorithm. The simulation results show that, under the condition of the same bandwidth, the convergence rate of the proposed optimization algorithm can be improved by adjusting the parameters of the quantizer. Therefore, the proposed optimization algorithm is more suitable for practical applications by weakening the assumptions on the adjacency matrix and the requirement of the network bandwidth.

Key words: distributed optimization, unbalanced digraph, switching network, uniform quantizer, non-quadratic Lyapunov function, subgradient algorithm

摘要： 由于已有的分布式次梯度算法大多基于理想的假设：网络拓扑是有向平衡的，构成网络的个体间通信的是各个个体某个状态变量的完全精确的信息。针对更一般的非平衡切换网络以及实际生活中网络通道的带宽限制，提出一种基于有限量化信息通信的切换网络分布式量化次梯度优化算法。在非平衡切换网络中，通过设计具有有限量化水平的一致量化器使所有信息在发送之前都经过量化，利用非二次李雅普诺夫函数方法，证明了所提出的多个体分布式量化次梯度优化算法的收敛性。最后仿真实例验证了所提算法的有效性，而且通过调节量化水平参数，在相同的带宽条件下，可提高信息传输速率，使网络中的个体更快地达到一致。该方法弱化了对刻画网络拓扑的邻接矩阵的假设及对网络带宽的要求，更具实用性。

关键词: 分布式优化, 非平衡有向图, 切换网络, 一致量化器, 非二次李雅普诺夫函数, 次梯度算法