An improved contraction method for structured monotone variational inequalities

For solving monotone variational inequalities with separate structures, Ye and Yuan [A descent method for stuctured monotone variational inequalities, Optim. Methods Softw. 22 (2007), 329-338] used the iterates generated by the well-known alternating directions method to design a descent direction, and thus presented a contraction method. This article continues on this study. By observing an improved descent direction and, selecting the corresponding optimal step sizes, a new contraction method is presented. In addition to proving the algorithm's convergence under mild assumptions, we compare the improved contraction method to Ye and Yuan's method (which is generalized) and achieve the superiority of the new method in theoretical senses.