A globally and superlinearly convergent quasi-Newton method for general box constrained variational inequalities without smoothing approximation

A new quasi-Newton algorithm for the solution of general box constrained variational inequality problem (GVI( l , u , F , f )) is proposed in this paper. It is based on a reformulation of the variational inequality problem as a nonsmooth system of equations by using the median operator. Without smoothing approximation, the proposed quasi-Newton algorithm is directly applied to solve this class of nonsmooth equations. Under appropriate assumptions, it is proved that the algorithmic sequence globally and superlinearly converges to a solution of the equation reformulation and also of GVI( l , u , F , f ). Numerical results show that our new algorithm works quite well.