Regularized Newton Methods for Monotone Variational Inequalities with H\"older Continuous Jacobians

This paper considers the problems of solving monotone variational inequalities with H\"older continuous Jacobians. By employing the knowledge of H\"older parameter $\nu$, we propose the $\nu$-regularized extra-Newton method within at most $\mathcal O(\epsilon^{-2/(2+\nu)})$ iterations to obtain an $\epsilon$-accurate solution. In the case of $\nu$ is unknown, we propose the universal regularized extra-Newton method within $\mathcal O(\epsilon^{-4/(3(1+\nu))})$ iteration complexity.