Convex Duality in Perturbed Utility Route Choice

Mogens Fosgerau and Jesper R. -V. S{\o}rensen

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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.

Date: 2026-04
New Economics Papers: this item is included in nep-dcm, nep-net and nep-tre
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