Numerical comparison between prediction-correction methods for general variational inequalities

In this paper, we propose two prediction-correction methods for solving general variational inequalities. The first method makes use of a descent direction to produce the new iterate while the second method generates the corrector by the improved extragradient method. Under certain conditions, the global convergence of both methods is proved. It is proved theoretically that the lower-bound of the progress obtained by the second method is greater than that by the first one. Numerical results are given to verify and compare the numerical efficiency of these two predictor-corrector methods.