@Article{CiCP-10-5,
author = {},
title = {An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1113--1131},
abstract = {<p style="text-align: justify;">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 Wardrop&#39;s 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 outperforms
the subgradient marching method for computing such equilibrium metrics.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.020210.311210a},
url = {https://global-sci.com/article/80957/an-adjoint-state-method-for-numerical-approximation-of-continuous-traffic-congestion-equilibria}
}