Levenberg–Marquardt method for solving systems of absolute value equations

In this paper, we suggest and analyze the Levenberg–Marquardt method for solving system of absolute value equations Ax−|x|=b, where A∈Rn×n,b∈RnA∈Rn×n,b∈Rn and x∈Rnx∈Rn are unknown. We present different line search methods to convey the main idea and the significant modifications. We discuss the convergence of the proposed method. We consider numerical examples to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction.