A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-Newton method

In this paper we propose a new unconstrained differentiable merit function f for box constrained variational inequality problems VIP(l, u, F). We study various desirable properties of this new merit function f and propose a Gauss-Newton method in which each step requires only the solution of a system of linear equations. Global and superlinear convergence results for VIP(l, u, F) are obtained Key results are the boundedness of the level sets of the merit function for any uniform P-function and the superlinear convergence of the algorithm without a nondegeneracy assumption. Numerical experiments confirm the good theoretical properties of the method.