Dual extrapolation and its applications for solving variational inequalities and related problems

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators (O(1/e)iterations), and for the operators with bounded variations(0 (1/e2)). Our technique can be applied for solving non smooth convex minimization problems with known structure. In this case the worst-case complexity bound is 0(1/e)iterations.