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We consider a network equilibrium model (i.e. a combined model), which wasproposed as an alternative to the classic four-step approach for travelforecasting in transportation networks. This model can be formulated as aconvex minimization program. We extend the combined model to the case of thestable dynamics (SD) model in the traffic assignment stage, which imposesstrict capacity constraints in the network. We propose a way to solvecorresponding dual optimization problems with accelerated gradient methods andgive theoretical guarantees of their convergence. We conducted numericalexperiments with considered optimization methods on Moscow and Berlin networks.

Primal-Dual Gradient Methods for Searching Network Equilibria in Combined Models with Nested Choice Structure and Capacity Constraints