Two-step inertial Tseng’s extragradient method for solving quasimonotone variational inequalities

We focus on quasimonotone variational inequality problems with non-Lipschitz operator and combine some operator theory techniques to establish a weak convergent fixed point iterative method to approximate the solution of the presented problems. The convergence analysis assumes very mild conditions and strictly weaker assumption on the cost operator associated with the problems and thus generalizes and extend recent related results in the literature. Finally, several numerical examples illustrate the potential and advantages of the proposed algorithm over some existing methods are presented.