Extrapolation From the Past Method for Variational Inequalities in a Hilbert Space

Abstract

The article considers variational inequalities with operators acting in a Hilbert space. For these problems, variants of the Extrapolation from the Past method have been proposed and studied. A sub-linear efficiency estimate for the gap function is proved. The strong convergence of the Extrapolation from the Past method for variational inequalities with uniformly monotone operators is proved. The linear rate of convergence of the Extrapolation from the Past method for variational inequalities with operators satisfying the generalized strong monotonicity condition is proved. An adaptive version of the algorithm is proposed. Regularized variants of the algorithm are proposed and theorems on their strong convergence are proved.