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This paper studies overdetermined system of absolute value equations (AVE) where data are contaminated by noise. The primary goal of this paper is to present a class of smoothing methods for optimal error correcting of AVE. To prove the feasibility of this non linear system, we adopt the minimal correction using the l2 norm by applying changes to the right hand vector. We demonstrate that the formulation of this problem as an unconstrained optimization problem using a quadratic objective function is possible. We then outline the algorithm and convergence analysis and propose a Newton method type for solving unconstrained optimization problem. Numerical results are provided to reveal the effectiveness of our method. [ABSTRACT FROM AUTHOR]