A Smoothing Technique for the Minimum Norm Solution of Absolute Value Equation

One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have infinitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. By applying the augmented Lagrangian method, this problem can be reduced to an unconstrained optimization problem with once differentiable objective function. To use Newton method, we apply the smoothing techniques. Computational results show that convergence to high accuracy often occurs in just a few iterations.