Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem

Evgenia Gasnikova; Alexander Gasnikov; Demyan Yarmoshik; Meruza Kubentaeva; Michael Persiianov; Irina Podlipnova; Ekaterina Kotlyarova; Ilya Sklonin; Elena Podobnaya; Vladislav Matyukhin

arXiv · 2305.09069

Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem

Evgenia Gasnikova·Alexander Gasnikov·Demyan Yarmoshik·Meruza Kubentaeva·Michael Persiianov·Irina Podlipnova·Ekaterina Kotlyarova·Ilya Sklonin·Elena Podobnaya·Vladislav Matyukhin

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Abstract

In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or Nesterov--de Palma). For the traffic assignment stage we use dual reformulation and combine these stages as a saddle-point problem (convex-concave). Then we discuss how one can solve this problem numerically.

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Evgenia Gasnikova, Alexander Gasnikov, Demyan Yarmoshik, Meruza Kubentaeva, Michael Persiianov, Irina Podlipnova, Ekaterina Kotlyarova, Ilya Sklonin, Elena Podobnaya, Vladislav Matyukhin. 2023-05-29. Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem. https://arxiv.org/abs/2305.09069

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