Absolute value equation solution via concave minimization

The NP-hard absolute value equation (AVE) Ax - vertical bar x vertical bar = b where A is an element of R-nxn and b is an element of R-n is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100, 000 equations.