Given a set in a finite-dimensional Euclidean space, and a function from this Euclidean space to itself, a variational inequality is to find a point in the given set, so that the function value evaluated at this point is a normal vector to the set at this point. Variational inequalities provide a unified mathematical model

for a large number of problems. This can be a force equilibrium that describes the dynamics of mechanical equipment, or a traffic equilibrium that predicts transportation network flows, or an economic equilibrium that predicts commodity prices, sector activities and consumer consumptions. Variational inequalities are also closely related to nonlinear optimization problems. This talk will start with an overview of several aspects of variational inequalities, followed by a discussion of our understanding of their solution properties with respect to data perturbation.

Shu Lu received her B.S. (2000) and M.S. (2002) degrees in Civil Engineering from Tsinghua University, and then obtained M.S. degrees in Industrial Engineering (2006) and Mathematics (2006) and a Ph.D. in Industrial Engineering (2007) at the University of Wisconsin-Madison. She is an assistant professor at the Department of Statistics and Operations Research, the University of North Carolina at Chapel Hill. Her research interests are in the area of mathematical optimization, especially on variational inequalities and variational analysis.