A modified alternating projection based prediction–correction method for structured variational inequalities

Abstract

In this paper, we propose a novel alternating projection based prediction–correction method for solving the monotone variational inequalities with separable structures. At each iteration, we adopt the weak requirements for the step sizes to derive the predictors, which affords fewer trial and error steps to accomplish the prediction phase. Moreover, we design a new descent direction for the merit function in correction phase. Under some mild assumptions, we prove the global convergence of the modified method. Some preliminary computational results are reported to demonstrate the promising and attractive performance of the modified method compared to some state-of-the-art prediction–contraction methods.