Universal method of searching for equilibria and stochastic equilibria in transportation networks

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.