A hybrid algorithm for solving the absolute value equation

We propose a hybrid algorithm for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving iteratively a linear system of equations followed by a linear program. The algorithm was tested on 100 consecutively generated random solvable instances of the AVE with n =50, 100, 200, 500 and 1,000. The algorithm solved 100% of the test problems to an accuracy of 10 by solving an average of 2.77 systems of linear equations and linear programs per AVE.