On Accelerated Coordinate Descent Methods for Searching Equilibria in Two-Stage Transportation Equilibrium Traffic Flow Distribution Model

N. A. Il'tyakov, M. A. Obozov, I. M. Dyshlevski, Demyan Yarmoshik, M. B. Kubentaeva, Alexander V. Gasnikov, Evgenia Gasnikova

Abstract: The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, it is proposed to use the accelerated block-coordinate Nesterov–Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can appreciably improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out.