Primal-dual gradient methods for searching network equilibria in combined models with nested choice structure and capacity constraints

Meruza Kubentayeva, Demyan Yarmoshik, Michael Persiianov, Alexey Kroshnin, Ekaterina Kotliarova, Nazarii Tupitsa, Dmitry Pasechnyuk, Alexander V. Gasnikov, Vladimir Shvetsov, Leonid Baryshev, Alexey Shurupov

Abstract: We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.