Convergence Rate of the Extrapolation from the Past and Operator Extrapolation Algorithms

The authors consider variational inequalities in the Hilbert space and two algorithms for their approximate solution: extrapolation from the past and operator extrapolation. Both algorithms have less computationally expensive iterations than the the classical extragradient algorithm: only one operator computation rather than two is needed. Non-asymptotic linear convergence rate estimates are proved for the variational inequalities with the Lipschitz continuous operators satisfying the generalized strict monotonicity condition. The results are new and improve the available estimates.