This paper proposes a distributed discrete-time algorithm to solve an additive cost optimization problem over undirected deterministic or time-varying graphs. Different from most previous methods that require to exchange exact states between nodes, each node in our algorithm needs only the sign of the relative state between its neighbors, which is clearly one bit of information. Our analysis is based on optimization theory rather than Lyapunov theory or algebraic graph theory. The latter is commonly used in existing literature, especially in the continuous-time algorithm design, and is difficult to apply in our case. Besides, an optimization-theory-based analysis may make our results more extendible. In particular, our convergence proofs are based on the convergences of the subgradient method and the stochastic subgradient method. Moreover, the convergence rate of our algorithm can vary from O(1/ln(k)) to O(1/√k), depending on the choice of the stepsize. A quantile regression problem is included to illustrate the performance of our algorithm using simulations.
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机译:分离的核酸(多核苷酸),反义寡核苷酸,抑制或减少编码CO2SEN蛋白的消息和/或CO2SEN蛋白或植物多聚核苷酸和多肽多糖的植物植株的表达的方法植物保护细胞,植物细胞,植物片,植物组织或植物,植物的一部分的碳吸收量和碳排量的负,正调节及增加,碳保护层和水流以及CO 2 / CO 2交换水交换或损失水开放植物,关闭植物的气孔,部分植物,器官,植物片或植物细胞,以增强或优化植物,植物片,器官,植物,植物的一部分上的生物量积累,植物,种子或植物细胞中的植物细胞或种子,板温度的降低和蒸腾强度的提高,降低了T型保护细胞中的效率降低和碳含量