半分布式forward-reflected-Douglas-Rachford分裂算法求解广义纳什平衡点

Semi-distributed forward-reflected-Douglas-Rachford splitting method for generalized Nash equilibrium seeking

中文关键词  广义纳什平衡点  半分布式  三算子分裂算法  多智能体系统

英文关键词  generalized Nash equilibrium  semi--distributed  three--operator splitting method  multi--agent systems

中文摘要

      针对多个体参与的广义纳什平衡点的求解问题, 已有算法通常都是基于两算子分裂算法forward--backward splitting. 本文基于三算子分裂算法forward--reflected--Douglas--Rachford(FRDR) splitting, 提出一种半分布式的FRDR算法. 半分布式旨在强调对偶变量的信息交换总是按照分布式的方式进行. 该算法有如下特性: 可以实现邻点映射和投影映射分别计算; 不需要假设伪梯度映射是协强制的或者强单调的; 通过存储上一轮交换的信息, 可以做到所需信息在每一轮迭代中只进行一次交换. 同时, 论文给出了有关迭代残差的收敛速率, 并通过数值仿真验证了所提算法的有效性.

英文摘要

      To deal with generalized Nash equilibrium seeking problems for multiple agents, existing methods are designed mainly based on the two--operator splitting approach, e.g. forward--backward splitting. In this paper, a semi--distributed method is proposed by turning to the three--operator splitting procedure, i.e. forward--reflected--Douglas--Rachford splitting(FRDR). It means that the information of dual variables are interchanged in a distributed way. The semi--distributed FRDR method has a threefold characterization. First, the computation of proximal mapping and projection mapping is separated. Second, the pseudogradient mapping is no longer assumed to be cocoercive or strongly monotone. Third, with the storage of interchanged information from last round, all needed information is interchanged only once at each iterating round. In addition, convergence rate is given in terms of iteration residual. Simulation results are also provided to illustrate the effectiveness of the method.