A modified augmented Lagrangian method for a class of monotone variational inequalities

The augmented Lagrangian method is an attractive approach for solving linearly constrained convex optimization problems (CCOP). The method is iterative and the task in each iteration is to solve a (convex optimization) sub-problem whose dimension is equal to the number of variables. For large problems, solving such a sub-problem can be still very expensive. In this paper, we propose a modified augmented Lagrangian method for a class of monotone variational inequalities which include CCOP. The computational load in each iteration of the proposed method is quite small. In order to demonstrate the ability and efficiency of the proposed method, we present some numerical results for convex nonlinear programming and traffic network equilibrium problems.