An inexact alternating direction method for solving a class of structured variational inequalities

The alternating direction method is mainly adopted to solve large-scale variational inequality problems with separable structure. The method is effective because it solves the original high-dimensional variational inequality problem by solving a series of much easier low-dimensional subproblems. In this paper, we present an inexact alternating directions method. Compared with the quadratic proximal alternating direction methods, the proposed method solves a series of related systems of nonlinear equations instead of a series of sub-VIs. The inexact criteria are more relaxed than the ones used by He et al. [7]. The generated sequence is Fejér monotone with respect to the solution set and the convergence is proved under suitable conditions.