Sensitivity analysis of aggregated variational inequality problems, with application to traffic equilibria

Some instances of variational inequality models over polyhedral sets can be stated in a disaggregated or aggregated formulation related by an affine variable transformation. For such problems, we establish that sensitivity analysis results under parameterizations rely neither on the strict monotonicity properties of the problem in terms of the disaggregated variables, nor on any particular choice of their values at the solution. We show how to utilize the affine transformation to devise computational tools for calculating sensitivity results and apply them to the sensitivity analysis of elastic demand traffic equilibrium problems. The results reached show that sensitivity results do not rely on the choice of any particular route or commodity flow solution. Further, the sensitivity analysis, including the calculation of the gradient of the equilibrium link flow if it exists, can be performed by means of solving linearized traffic equilibrium problems.