Novel self-adaptive inertial scheme for variational inequalities

We propose a novel self-adaptive inertial algorithm for solving variational inequality, where the underlying function is continuous and fulfills a certain pseudomonotonicity assumption. With inertial term only one orthogonal projection onto the feasible set is computed in each iteration, thereby accelerating the convergence rate of the algorithm. Interestingly, the proposed algorithm does not require knowledge of the Lipschitz constant, as it is rarely known in practice. Under some conditions we show that the iterations produced by the algorithm converge weakly and strongly in real Hilbert spaces. Finally, to support our analysis a computational experience is reported and the trust of the method is compared with another method in the literature.