TY - JOUR
T1 - Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium
AU - Friesz, Terry L.
AU - Han, Ke
AU - Bagherzadeh, Amir
N1 - Publisher Copyright:
© 2021
PY - 2021/8
Y1 - 2021/8
N2 - In this paper we present sufficient conditions for convergence of projection and fixed-point algorithms used to compute dynamic user equilibrium with elastic travel demand (E-DUE). The assumption of strongly monotone increasing path delay operators is not needed. In its place, we assume path delay operators are merely weakly monotone increasing, a property assured by Lipschitz continuity, while inverse demand functions are strongly monotone decreasing. Lipschitz continuity of path delay is a very mild regularity condition. As such, nonmonotone delay operators may be weakly monotone increasing and satisfy our convergence criteria, provided inverse demand functions are strongly monotone decreasing. We illustrate convergence for nonmonotone path delays via a numerical example.
AB - In this paper we present sufficient conditions for convergence of projection and fixed-point algorithms used to compute dynamic user equilibrium with elastic travel demand (E-DUE). The assumption of strongly monotone increasing path delay operators is not needed. In its place, we assume path delay operators are merely weakly monotone increasing, a property assured by Lipschitz continuity, while inverse demand functions are strongly monotone decreasing. Lipschitz continuity of path delay is a very mild regularity condition. As such, nonmonotone delay operators may be weakly monotone increasing and satisfy our convergence criteria, provided inverse demand functions are strongly monotone decreasing. We illustrate convergence for nonmonotone path delays via a numerical example.
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U2 - 10.1016/j.trb.2021.01.007
DO - 10.1016/j.trb.2021.01.007
M3 - Article
AN - SCOPUS:85110167058
VL - 150
SP - 336
EP - 352
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
SN - 0191-2615
ER -