Augmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform absolute value equation to linear system and then demonstrate efficient augmented Lagrangian method to solve the linear system. Also this paper is considered a class of two-point boundary value problems and introduced a new method to solve them. In this paper is shown that this class of problems is equivalent to absolute value equation. To illustrate the feasibility and effectiveness our method we generate random problems and solve them also solve a class of two-point boundary value problems. In section numerical results, we consider the efficiency of the proposed method. Computational results show that convergence to high accuracy often occurs in short time.