We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problemswhose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian methodfor constrained optimization. At each iteration, primal variables are updated by solvingan unconstrained variational inequality problem, and then dual variables are updated through a closed formula.A full convergence analysis is provided, allowing for inexact solution of the subproblems.
