Sensitivity Analysis of Variational Inequalities Over Aggregated
Polyhedra, with Application to Traffic Equilibria

Michael Patriksson
Department of Mathematics 
Chalmers University of Technology 
S-412 96 Gothenburg,
Sweden

R. Tyrrell Rockafellar
Department of Mathematics 
University of Washington
Seattle, WA 98195-4350

ABSTRACT:

Some instances of variational inequality models over polyhedral sets
can be stated by either using disaggregated variables or using
aggregated variables through an affine transformation. For such
problems, we establish that sensitivity analysis results under ample
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.

   
Key words: Disaggregated representation; aggregated representation;
ample parameterization; sensitivity analysis; locally Lipschitz
function; directional derivative; critical cone; Wardrop; traffic
equilibrium.