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

摘要

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 ( $O({1 over epsilon})$ iterations), and for the operators with bounded variations ( $O({1 over epsilon^2})$ iterations). Our technique can be applied for solving non-smooth convex minimization problems with known structure. In this case the worst-case complexity bound is $O({1 over epsilon})$ iterations.