A Multi-Convex Approach to Latency Inference and Control in Traffic Equilibria From Sparse Data

A common behavioral assumption in the modeling of traffic networks is the user equilibrium. Since traffic volumes, resulting from the rational behavior of agents, are easily but sparsely observable, and delay functions are not directly observable, we present a mathematical program with equilibrium constraint (MPEC) framework to impute the delay functions and centrally control the system from partial observations of equilibria. We also develop a novel method for solving MPECs using multi-convex optimization. Our block descent method has an intuitive interpretation, and numerical experiments demonstrate its accuracy for structural estimation, and highlight the importance of sensor placement for toll pricing.