Augmented Lagrangian Method for Finding Minimum Norm Solution to the Absolute Value Equation

‎In this paper‎, ‎we give an algorithm to compute the minimum 1norm solution to the absolute value equation (AVE)‎. ‎The augmented Lagrangian method is investigated for solving this problems‎ . ‎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.