This paper presents a new inexact parallel splitting method for solving variational inequalities (VIs) with separable structures. To solve VIs, some classical methods augmented Lagrangian method and alternating direction method of multipliers (ADMM) were presented, but they require solving sub-VIs exactly. However, these sub-VIs could be too difficult or impossible to be solved exactly in many practical applications. Recently, an inexact alternating direction method (IADM) was proposed in Chen (J Optim Theory Appl,2014,163:439). But when the dimensionality of data is tremendous large, parallel splitting method (PSM) is more efficient than ADMM. So based on IADM, we proposed a new inexact parallel splitting method (NIPSM). Convergence of the new method is proved under mild assumptions and some numerical results demonstrate that the new method NIPSM is efficient.
