Convex Duality in Perturbed Utility Route Choice
Theoretical Economics
2026-04-23 v1
Abstract
This paper develops a highly general convex duality framework for the perturbed utility route choice (PURC) model. We show that the traveler's constrained, potentially non-smooth utility maximization problem admits a dual formulation: an unconstrained concave maximization problem with a differentiable objective. The unique optimal flow can be recovered link-by-link from any dual solution via the convex conjugates of link perturbation functions. These properties enable efficient gradient-based optimization for large-scale networks and fast computation for sensitivity analysis. Finally, the framework reveals a structural analogy between PURC and current flow in electrical circuits.
Cite
@article{arxiv.2604.20220,
title = {Convex Duality in Perturbed Utility Route Choice},
author = {Mogens Fosgerau and Jesper R. -V. Sørensen},
journal= {arXiv preprint arXiv:2604.20220},
year = {2026}
}