Convex Duality in Perturbed Utility Route Choice

2026-04-22

AI Summary

This study addresses the non-smooth, constrained user utility maximization problem inherent in Perturbed Utility Route Choice (PURC) models by introducing a unified convex duality framework. The proposed approach transforms the original problem into an unconstrained, differentiable concave maximization task, enabling efficient gradient-based optimization. By leveraging the convex conjugate of link-specific perturbation functions, the method uniquely recovers optimal route flows link-by-link. This work establishes, for the first time, a rigorous convex duality theory for PURC models, revealing a structural analogy to electrical current flows. The framework facilitates rapid sensitivity analysis and scalable computation, significantly enhancing both efficiency and applicability for real-time solution and parameter sensitivity evaluation in large-scale, complex transportation networks.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• perturbed utility route choice
• convex duality
• utility maximization
• non-smooth optimization
• traffic assignment

Innovation

• convex duality
• perturbed utility route choice
• convex conjugate
• gradient-based optimization
• structural analogy