Universal Method of Searching for Equilibria and Stochastic Equilibria in Transportation Networks

Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 1. P. 19–33.

Baimurzina D. R., Gasnikov A. V., Двуреченский П. Е., Ершов Е. И., Kubentaeva M. B., Lagunovskaya A. A.

A universal method of searching for usual and stochastic equilibria in congestion population games is proposed. The Beckmann and stable dynamics models of an equilibrium flow distribution over paths are considered. A search for Nash(–Wardrop) stochastic equilibria leads to entropy-regularized convex optimization problems. Efficient solutions of such problems, more exactly, of their duals are sought by applying a recently proposed universal primal-dual gradient method, which is optimally and adaptively tuned to the smoothness of the problem under study. © 2019, Pleiades Publishing, Ltd.

Ключевые слова: dual problem, public transportation networks, Beckmann’s model, stable dynamics model, transportation flows, universal method of similar triangles