A projection-like method for quasimonotone variational inequalities without Lipschitz continuity

For most projection methods, the operator of a variational inequality problem is assumed to be monotone (or pseudomonotone) and Lipschitz continuous. In this paper, we present a projection-like method to solve quasimonotone variational inequality problems without Lipschitz continuity. Under some mild assumptions, we prove that the sequence generated by the proposed algorithm converges to a solution. Numerical experiments are provided to show the effectiveness of the method.