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

TL;DR

This paper introduces a universal primal-dual method based on Nesterov's approach to efficiently find traffic flow equilibria in transport networks, applicable even when the dual problem is non-smooth.

Contribution

It adapts the primal-dual Nesterov's Universal Method to solve equilibrium traffic flow problems, handling non-smooth dual problems effectively.

Findings

Method successfully finds traffic equilibria in BMW and Stable Dynamic models.

Universal Method performs well on saddle-point problems in traffic modeling.

Applicable to non-smooth dual problems in transportation networks.

Abstract

We describe how primal-dual version of Nesterov's Universal Method (with one projection) can be applied to solve the dual problem for the problem of searching equilibrium traffic flow distribution in transport networks (BMW-model, Stable Dynamic model). We observe that although the dual problem isn't smooth Universal Methods works as it is Mirror Prox method and we consider saddle-point type problem.