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Convex Duality in Perturbed Utility Route Choice

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

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.

Suggested Citation

  • Mogens Fosgerau & Jesper R. -V. S{o}rensen, 2026. "Convex Duality in Perturbed Utility Route Choice," Papers 2604.20220, arXiv.org.
    • Handle: RePEc:arx:papers:2604.20220
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    File URL: http://arxiv.org/pdf/2604.20220
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