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This paper is concerned with dynamic user equilibrium with elastic traveldemand (E-DUE) when the trip demand matrix is determined endogenously. Wepresent an infinite-dimensional variational inequality (VI) formulation that isequivalent to the conditions defining a continuous-time E-DUE problem. Anexistence result for this VI is established by applying a fixed-point existencetheorem (Browder, 1968) in an extended Hilbert space. We present threealgorithms based on the aforementioned VI and its re-expression as adifferential variational inequality (DVI): a projection method, a self-adaptiveprojection method, and a proximal point method. Rigorous convergence resultsare provided for these methods, which rely on increasingly relaxed notions ofgeneralized monotonicity, namely mixed strongly-weakly monotonicity for theprojection method; pseudomonotonicity for the self-adaptive projection method,and quasimonotonicity for the proximal point method. These three algorithms aretested and their solution quality, convergence, and computational efficiencycompared. Our convergence results, which transcend the transportationapplications studied here, apply to a broad family of infinite-dimensional VIsand DVIs, and are the weakest reported to date.

Elastic demand dynamic network user equilibrium: Formulation, existence and computation