Convex Duality in Perturbed Utility Route Choice
Mogens Fosgerau, Jesper R. -V. Sørensen
TLDR
This paper introduces a convex duality framework for perturbed utility route choice, transforming a complex problem into an efficiently solvable one.
Key contributions
- Developed a general convex duality framework for the Perturbed Utility Route Choice (PURC) model.
- Transforms constrained, non-smooth utility maximization into a differentiable, unconstrained dual problem.
- Enables efficient gradient-based optimization for large-scale networks and fast sensitivity analysis.
- Reveals a structural analogy between PURC and current flow in electrical circuits.
Why it matters
This framework significantly improves the computational efficiency of route choice models, making them practical for large-scale transportation networks. It also offers new theoretical insights by drawing parallels to electrical circuit analysis.
Original 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.
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