A Finsler Geometrical Programming for the Nonlinear Complementarity Problem of Traffic Equilibrium

TL;DR

This paper introduces a Finsler geometric framework for modeling and solving nonlinear complementarity problems in traffic equilibrium, providing a novel approach to transportation system optimization.

Contribution

It develops a Finsler geometrical programming method and a dynamical model for traffic equilibrium problems, expanding geometric optimization techniques in transportation.

Findings

Finslerian model effectively captures traffic equilibrium dynamics

Provides a new geometric approach to nonlinear complementarity problems

Applicable to various transportation system management scenarios

Abstract

This work is a geometrical approach to the optimization problem motivated by transportation system management. First, an attempt has been made to furnish a comprehensive account of geometric programming based on the elementary Finsler geometry in $I\!\!R^n$. Then, a Finslerian dynamical model for the nonlinear complementarity problem of traffic equilibrium is presented that may be applied for different equilibrium problems.