Some Predict-Correct Projection Methods for Monotone Variational Inequalities

摘要

For solving nonlinear variational inequality problems, the explicit projectionmethod is simple, but it converges under strong assumptions. The implicit projection method is convergent under mild conditions, however, it has to solve a system of nonlinear equations in each iteration. It seems to be interesting to study predict-correct methods, which may exploit the advantages (or overcome the difficulties) of both explicit and implicit methods. This paper presents some predict-correct projection methods for solving monotone variational inequalities. The first method in this paper is based on convergence results of the inexact implicit projection methods. The second method uses a simple explicit method to make a prediction and utilizes the Douglas-Rachford method to make a correction. Finally, in numerical viewpoint, the authors propose a self-adaptive predict-correct method.