  In this paper we consider the application of several gradient methods to the
traffic assignment problem: we search equilibria in the stable dynamics model
(Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated
Frank--Wolfe algorithm widely used for the Beckmann model, these gradients
methods solve the dual problem and then reconstruct a solution to the primal
one. We deal with the universal gradient method, the universal method of
similar triangles, and the method of weighted dual averages, and estimate their
complexity for the problem. Due to the primal-dual nature of these methods, we
use a duality gap in a stopping criterion. In particular, we present a novel
way to reconstruct admissible flows (i.e.,\ meeting the capacity constraints
and induced by flows on the paths) in the stable dynamics model, which provides
us with a computable duality gap.
