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

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