In this paper, we consider the NP-hard problem of solving absolute value equation (AVE). We reformulate this problem as an horizontal linear complementarity problem and then use a smoothing technique to solve the problem as a sequence of concave minimization problem. This approach leads to a new method valid for a general equation without additional hypothesis on the set of solutions furthermore it remains valid as a method to solve the linear complementarity problem. We prove convergence to the original problem and an error estimate for the sequence of solutions. We also provide remarks about the algorithm and its implementation. The concave minimization problem are solved by considering a sequence of linear programs. Finally numerical results on randomly generated problems and applications are used to validate our approach and show its interest as in the general case it manages to reduce the number of unsolved problems compare to existing methods in the literature.