Solving strongly monotone variational and quasi-variational inequalities

In this paper we develop a new and efficientmethod for variational inequality with Lipschitzcontinuous strongly monotone operator. Our analysis isbased on a new strongly convex merit function. Weapply a variant of the developed scheme for solvingquasivariational inequalities. As a result, we significantlyimprove the standard sufficient condition for existenceand uniqueness of their solutions. Moreover, we get a newnumerical scheme, whose rate of convergence is much higherthan that of the straightforward gradient method.