多模式交通均衡问题的一阶分裂算法

First-order splitting algorithm for multi-model traffic equilibrium problems

本文研究包含私人交通和公共交通工具的多模式交通均衡问题,将其建模成带线性不等式约束的可分单调变分不等式问题,并提出一种修正的交替方向乘子法进行求解。通过适当地修改子问题并加上一个简单的校正步,提出一种针对线性不等式约束问题的并行求解算法。在一般的假设条件下,证明了这个新算法的全局收敛性和次线性收敛速度,并把算法应用到交通模型中。

In this paper,we study the multi-model traffic equilibrium problem of private transportation and public transportation,which is modeled as a separable monotonous variational inequality problem with linear inequality constraints.We propose a modified alternating direction method of multipliers in a parallel way for the linear inequality constraint problem by modifying the subproblem appropriately and adding a simple correction step.Under general hypothetical conditions,the global convergence and sublinear convergence rate of this new algorithm are proved.Applying the algorithm to the traffic equilibrium shows its effectiveness.