A Two-Stage Step Size Rule on Improved Prediction-Correction Method for Monotone Nonlinear Variational Inequalities

This paper proposes a two-stage step size rule for monotone nonlinear variational inequality (VI) problems to further extend the improved prediction-correction (PC) method. The improved PC method is one of the most popular methods for solving the monotone VI problem due to its simplicity and efficiency. To obtain a more exact and efficient step size in the proved PC method, the step size is calculated by two stages. The first stage is the prediction stage, in which the original step size rule in improved PC method is adopted. The second stage is the correction stage, in which the result in the prediction stage is used to achieve a more exact step size. The deduction of the two-stage step size rule is given. Numerical examples indicate that the improved PC method with the two-stage step size rule can save the CPU time compared with that without the two-stage step size rule.