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The search for equilibrium in a two-stage traffic flow model reduces to thesolution of a special nonsmooth convex optimization problem with two groups ofdifferent variables. For numerical solution of this problem, the paper proposesto use the accelerated block-coordinate Nesterov-Stich method with a specialchoice of block probabilities at each iteration. Theoretical estimates of thecomplexity of this approach can markedly improve the estimates of previouslyused approaches. However, in the general case they do not guarantee fasterconvergence. Numerical experiments with the proposed algorithms are carried outin the paper.

On accelerated coordinate descent methods for searching equilibria in two-stage transportation equilibrium traffic flow distribution model