Convex Duality in Perturbed Utility Route Choice

TL;DR

This paper introduces a convex duality framework for the perturbed utility route choice model, enabling efficient optimization and revealing structural analogies with electrical circuits.

Contribution

It develops a general duality approach for PURC, allowing unconstrained optimization and link-by-link flow recovery, advancing computational methods in network analysis.

Findings

Dual formulation simplifies the constrained utility maximization.

Flow can be recovered from dual solutions using convex conjugates.

Framework enables efficient gradient-based optimization and sensitivity analysis.

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.