A QP-free constrained Newton-type method for variational inequality problems

We consider a simply constrained optimization reformulation of the Karush-R uhn-Tucker conditions arising from variational inequalities. Based on this reformulation, we present a new Newton-type method for the solution of vari ational inequalities. The main properties of this method are: (a) it is wel l-defined for an arbitrary variational inequality problem, (b) it is global ly convergent at least to a stationary point of the constrained reformulati on, (c) it is locally superlinearly/quadratically convergent under a certai n regularity condition, (d) all iterates remain feasible with respect to th e constrained optimization reformulation, and (e) it has to solve just one linear system of equations at each iteration. Some preliminary numerical re sults indicate that this method is quite promising.