An adjoint state method for numerical approximation of continuous traffic congestion equilibria

Songting Luo Shing-Yu Leung Jianliang Qian

Numerical Analysis and Scientific Computing mathscidoc:1912.43191

Communications in Computational Physics, 10, (5), 1113-1131, 2011.11
The equilibrium metric for minimizing a continuous congested traffic model is the solution of a variational problem involving geodesic distances. The continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrops equilibrium. We propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous formulation. The method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium metric and the resulting geodesic distances. The geodesic distance needed for the state equation is computed by solving a factored eikonal equation, and the adjoint state equation is solved by a fast sweeping method. Numerical examples demonstrate that the proposed adjoint state method produces desired equilibrium metrics and
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@inproceedings{songting2011an,
  title={An adjoint state method for numerical approximation of continuous traffic congestion equilibria},
  author={Songting Luo, Shing-Yu Leung, and Jianliang Qian},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112838874118751},
  booktitle={Communications in Computational Physics},
  volume={10},
  number={5},
  pages={1113-1131},
  year={2011},
}
Songting Luo, Shing-Yu Leung, and Jianliang Qian. An adjoint state method for numerical approximation of continuous traffic congestion equilibria. 2011. Vol. 10. In Communications in Computational Physics. pp.1113-1131. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112838874118751.
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