A Row-Stochastic Event-Based Quantized Algorithm for Distributed Optimization With Linear Convergence

This article proposes the row-stochastic event-based quantized (RSEQ) algorithm to address the distributed optimization problem with multiple communication constraints, including limited communication costs and bandwidth. In RSEQ, a novel event-based dynamic quantizer is designed to resist the negative effects of communication constraints on the algorithm. The quantizer encompasses the event generator and the dynamic encoder/decoder, which collectively adapt the frequency and size of information sharing based on real-time state. The RSEQ only requires the construction of a row-stochastic weight matrix, which leads to lower conservatism compared to algorithms based on column-stochastic matrices. Additionally, the introduction of an acceleration term enables RSEQ to linearly converge to the globally optimal solution without the deployment of the average gradient estimator. Instead, a Perron vector estimator needs to be employed to counteract the unbalancedness of the directed network. With the effect of the event generator, the Perron vector estimator can also be left inactive after a certain number of iterations, which means that the transmission of only state information between agents can linearly converge to the global optimal solution under directed networks. Finally, the effectiveness of the algorithm is demonstrated through an economic dispatch problem in smart grids.