A new criterion for an inexact parallel splitting augmented Lagrangian method

In this paper, we study the computational method for solving the variational inequality problem with the separable structure and linear constraints. We propose a new relaxed inexact criterion and a prediction-correction approach in the inexact splitting parallel augmented Lagrangian methods, which make it easier to solve the resulting subproblems. Under a mild condition, we prove the global convergence and establish a worst-case convergence rate for the new inexact algorithm. Some numerical experiments show the effectiveness and feasibility of the new inexact method.