Sensitivity Analysis for Variational Inequalities Defined on Polyhedral Sets

Variational inequalities have often been used as a mathematical programming tool in modeling various equilibria in economics and transportation science. The behavior of such equilibrium solutions as a result of the changes in problem data is always of concern. In this paper, we present an approach for conducting sensitivity analysis of variational inequalities defined on polyhedral sets. We introduce the notion of differentiability of a point-to-set mapping and derive continuity and differentiability properties regarding the perturbed equilibrium solutions, even when the solution is not unique. As illustrated by several examples, the assumptions made in this paper are in a certain sense the weakest possible conditions under which the stated properties are valid. We also discuss applications to some equilibrium problems such as the traffic equilibrium problem.