传统的拥堵道路收费和近期提出的可交易电子路票等交通拥堵管理手段在数学上都可以表示成特殊的变分不等式。因此，变分不等式新的算法设计和理论分析是优化领域的研究热点之一。本项目主要针对交通均衡问题中的三类变分不等式模型进行理论和算法研究。首先，对拥堵道路收费中无容量约束的变分不等式模型，鉴于其算子部分未知的特点，设计单调算子的分裂算法并分析其全局收敛性；进一步借鉴机器学习技巧，设计加速的算子分裂方法并分析新算法的收敛性。其次，对拥堵道路收费中带容量约束的变分不等式模型，利用误差界条件证明预测校正方法的收敛率；采取Nesterov加速策略对预测校正方法进行加速，并分析其收敛性和收敛速度。最后，对可交易电子路票方案下的变分不等式模型，研究如何使试错方法有更宽松、实用的非精确准则，使得子问题容易求解，降低每步迭代的计算量。本项目是为交通均衡问题提供切实可行的算法，为管理者的决策提供一定的理论支撑。

Traditional congestion road pricing, recently proposed tradable credit schemes and other measures of traffic congestion management can be mathematically expressed as special variational inequalities. As a consequence, the new designing algorithms and analytical theory of variational inequalities are one of research hotspots in the field of optimization. This project mainly studies the theory and algorithms of three categories of variational inequality (VI for short) models of traffic equilibrium problems. Firstly, for the VI model corresponding to the road congestion pricing problem with no capacity constraints, we will propose the monotone operator splitting method for the oracle problem and prove their global convergence; by combining the idea of machine learning, we will further propose the accelerated operator splitting method, and establish the convergence. Secondly, for the VI model corresponding to the road congestion pricing problem with capacity constraints, we first prove the convergence rate of the prediction and correction method; then we will propose an accelerated prediction and correction method by using the Nesterov acceleration strategy and analyze the convergence and converging rate. Finally, for the VI model with the tradable credit schemes, by introducing some more relaxing and practical accuracy criteria, we will develop an inexact version of the trial and error approach, which makes the sub-problem easier to solve as well as reduces the computing cost of each iteration in the implementation. The project provides some achievable algorithms for traffic equilibrium problems and theoretical support to decision makers.