A reduction method for variational inequalities

This paper explains a method by which the number of variables in a variational inequality having a certain form can be substantially reduced by changing the set over which the variational inequality is posed. The method applies in particular to certain economic equilibrium problems occurring in applications. We explain and justify the method, and give examples of its application, including a numerical example in which the solution time for the reduced problem was approximately 2% of that for the problem in its original form. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.The research reported here was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number F49620-95-1-0222, and by the U.S. Army Research Office under grant number DAAH04-95-1-0149. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the sponsoring agencies or the U.S. Government.