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. (c) 2006 Elsevier Inc. All rights reserved.