  We present a method for dimensionality reduction of an affine variational
inequality (AVI) defined over a compact feasible region. Centered around the
Johnson Lindenstrauss lemma, our method is a randomized algorithm that produces
with high probability an approximate solution for the given AVI by solving a
lower-dimensional AVI. The algorithm allows the lower dimension to be chosen
based on the quality of approximation desired. The algorithm can also be used
as a subroutine in an exact algorithm for generating an initial point close to
the solution. The lower-dimensional AVI is obtained by appropriately projecting
the original AVI on a randomly chosen subspace. The lower-dimensional AVI is
solved using standard solvers and from this solution an approximate solution to
the original AVI is recovered through an inexpensive process. Our numerical
experiments corroborate the theoretical results and validate that the algorithm
provides a good approximation at low dimensions and substantial savings in time
for an exact solution.
