In this paper, we consider the NP-hard problem of solving absolute value equation (AVE). It is sometimes difficult to solve general (AVE) and our concern is to propose a new method, which reduces the number of unsolved problems. This approach leads to a new method valid for general (AVE). We transform (AVE) as an horizontal linear complementarity problem, then we reformulate it in a sequence of concave optimization problems. We show convergence to the original problem, an error estimate for the sequence of solutions. Moreover we give remarks about the algorithm, where we solve sequences of linear programs, and numerical results, which shows that this new method manages to improve the number of unsolved problems compare to usual one.