R-linear convergence analysis of inertial extragradient algorithms for strongly pseudo-monotone variational inequalities

Some extragradient-type algorithms with inertial effect for solving strongly pseudo-monotone variational inequalities have been proposed and investigated recently. While the convergence of these algorithms was established, it is unclear if the linear rate is guaranteed. In this paper, we provide R-linear convergence analysis for two extragradient-type algorithms for solving strongly pseudo-monotone, Lipschitz continuous variational inequality in Hilbert spaces. The linear convergence rate is obtained without the prior knowledge of the Lipschitz constants of the variational inequality mapping and the stepsize is bounded from below by a positive number. Some numerical results are provided to show the computational effectiveness of the algorithms.