Finite convergence of extragradient-type methods for solving variational inequalities under weak sharp condition

We prove the finite convergence of the sequences generated by some extragradient-type methods solving variational inequalities under the weakly sharp condition of the solution set. In addition, we provide estimations for the number of iterations to guarantee the sequence converges to a point in the solution set and prove that these estimations are optimal. Numerical examples are presented to illustrate the theoretical results.