This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Lu, S. Articles by Robinson, S. M. Search for Related Content

Variational Inequalities over Perturbed Polyhedral Convex Sets

Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599
Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706
shulu{at}email.unc.edu, http://www.unc.edu/shulu/
smrobins{at}wisc.edu, http://www.engr.wisc.edu/ie/faculty/robinson_stephen.html

This paper provides conditions for existence of a locally unique, Lipschitzian solution of a linear variational inequality posed over a polyhedral convex set in n under perturbation of either or both of the constant term in the variational inequality and the right-hand side of the system of linear constraints defining its feasible set. Conditions for perturbation of just the constant term are well known. Here we show that a suitable extension of those conditions suffices for the more general case in which the right-hand side of the constraints varies also. As a consequence, we obtain existence, uniqueness, and Lipschitz continuity properties of solutions of nonlinear variational inequalities posed over perturbed polyhedral convex sets.

Key Words: variational inequality; sensitivity; coherent orientation; polyhedral convex set; polyhedral multifunction; normal manifold
History: Received: May 16, 2006; revision received: August 16, 2007;