A Preconditioner for Solving Large Scale Variational Inequality Problems

The numerical solution of a large scale variational inequality problem can be obtained by a generalization of a Inexact Newton method applied to a semismooth nonlinear system. This approach requires to solve at each step a sparse and large linear system. In this work we obtain an approximate solution of this system by the LSQR algorithm combined with a convenient preconditioner that is a variant of the incomplete LU-factorization. We propose a preconditioner that admits a block-factorization. Numerical experiments on a set of test-problems show the effectiveness of this approach.