A Jacobian smoothing method for box constrained variational inequality problems

In this paper we propose a Jacobian smoothing algorithm for the solution of the box constrained variational inequality problems VIP(l,u,F). The algorithm is based on a reformulation of a semismooth system of equations by using the Fischer-Burmeister function h(a,b)=a2+b2−a−b. Global and local superlinear convergence results for VIP(l,u,F) are obtained. Numerical experiments confirm the good theoretical properties of the algorithm.