Universal similar triangulars method for searching equilibriums in traffic flow distribution models

Primal-dual method for searching equillibriums in mixed traffic assignment problems

We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover the solution of the primal problem. First technique is based on "models" approach and second one is based on Lagrange multiplyers technique. Both approaches have its own advantages and drawbacks. We discuss them.

关于两阶段交通平衡交通流分配模型中搜索平衡的加速坐标下降方法

On accelerated coordinate descent methods for searching equilibria in two-stage transportation equilibrium traffic flow distribution model

针对两阶段交通流模型平衡搜索对应的非光滑凸优化问题，提出带特殊块概率选取的加速块坐标Nesterov-Stich方法，其理论复杂度更优且开展了数值实验。

About reduction of searching competetive equillibrium to the minimax problem in application to different network problems

In the paper we show that an important class of multistage traffic equillibrium models (including correspondence matrix calculation, traffic assignment problem etc) and their economic generalizations can be considered as proper population games with the minimax structure of equillibriums. This is not trivial because at the first sight we have to consider competetive (Valras) equilibrium and Nash-Vardroop equillibrium.

Searching equillibriums in large transport networks

In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different numerical approaches for this problem.

Efficient numerical methods for searching equillibriums in large transport networks

We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding numerical algorithms that allows us to combine the optimal method from the basis ones and predescribed operations on methods.

具有嵌套选择结构和容量约束的组合模型中搜索网络均衡的原对偶梯度方法

Primal-Dual Gradient Methods for Searching Network Equilibria in Combined Models with Nested Choice Structure and Capacity Constraints

本文扩展了网络均衡组合模型，在交通分配阶段引入稳定动力学模型以施加严格容量约束，提出基于加速梯度方法的对偶优化求解途径并给出收敛性理论保证，在莫斯科和柏林网络上进行了数值实验验证。