Strong Convergence of the Regularized Operator Extrapolation Algorithm For Variational Inequalities

The authors propose and investigate a new algorithm for solving variational inequalities in Hilbert spaces. The proposed iterative algorithm is regularized by the operator extrapolation method using the Halpern scheme. In terms of the amount of computation required for the iterative step, the algorithm has an advantage over the Korpelevich extragradient method and the method of extrapolation from the past. For variational inequalities with monotone, Lipschitz continuous operators acting in Hilbert space, a theorem on the strong convergence of the method is proved.