Primal-Dual Method for Searching Equilibrium in Hierarchical Congestion Population Games

С. 584–595.

Dvurechensky P., Gasnikov A., Gasnikova E., Matsievsky S., Rodomanov A., Usik I.

In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

Keywords: entropy, энтропия, equilibrium, сложность алгоритма, равновесие, двойственная задача, dual problem, выпуклая оптимизация, algorithm complexity, primal-dual method, logit dynamics, multistage model of traffic flows, прямо-двойственный метод, логит-динамика, многостадийная модель транспортных потоков, convex optimization

In book

Proceedings of DOOR 2016 Conference, special issue of CEUR Workshop Proceedings

Vol. 1623. , CEUR Workshop Proceedings, 2016.