Augmented Lagrangian method for nding minimum norm solution to the absolute value equation

In this paper, we give an algorithm to compute the minimum 1-norm solution to the absolute value equation (AVE). The augmented Lagrangian method is investigated for solving this problem. This approach leads to an unconstrained minimization problem with once differentiable convex objective function. We propose a quasi-Newton method for solving unconstrained optimization problem. Computational results show that convergence to high accuracy often occurs in just a few iterations.