A New Projection-Type Alternating Direction Method for Monotone Variational Inequality Problems

In this paper, we design a new projection-type alternating direction method which is an attractive method for solving variational inequality problems, and its application range covers linear programming, semidefinite programming etc. In each iteration, it just solves a linear equation and implements three orthogonal projections to closed convex sets. Under the conditions of monotonicity and Lipschitz continuity of f(x) involved in the variational inequality problems, we prove the global convergence of the new method.