Absolute value equation solution via dual complementarity

By utilizing a dual complementarity condition, we propose an iterative method for solving the NPhard 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 a succession of linear programs. The algorithm was tested on 500 consecutively generated random solvable instances of the AVE with n =10, 50, 100, 500 and 1,000. The algorithm solved 90.2% of the test problems to an accuracy of 10 .