An extended alternating direction method for variational inequality problems with linear equality and inequality constraints

Recently, some modified alternating direction methods have been proposed to solve a class of nonlinear variational inequality problems with linear equality constraints. These methods are more efficient than the classical one since they only need some orthogonal projections onto a simple set and some function evaluations per iteration. In this paper, we propose an extended alternating direction method to solve a more general nonlinear monotone variational inequality problem with both linear equality and inequality constraints. The proposed method only needs one additional projection to a simple set to handle the inequality constraints directly. Global convergence is provided along with numerical results of two applications to demonstrate the efficiency and robustness of the proposed method.