SAMS Subject Classification Number: 11

In this work we seek to establish a simple iterative method for solving quasimonotone variational inequalities, that are more general than the classical monotone version. While the few existing results are only weak convergence methods under quite restrictive conditions, we present a new Mann-type inertial projection and contraction method for solving quasimonotone variational inequalities as well as variational inequalities without monotonicity. Under standard assumptions, we prove a strong convergence result for our method. We also present several numerical examples to illustrate the simplicity and computational advantages of our proposed scheme over existing methods in literature.