Minimum Norm Solution to the Absolute Value Equation in the Convex Case

In this paper, we give an algorithm to compute the minimum norm solution to the absolute value equation (AVE) in a special case. We show that this solution can be obtained from theorems of the alternative and a useful characterization of solution sets of convex quadratic programs. By using an exterior penalty method, this problem can be reduced to an unconstrained minimization problem with once differentiable convex objective function. Also, 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.