A corrected Levenberg–Marquardt algorithm with a nonmonotone line search for the system of nonlinear equations

In this paper, we propose a corrected Levenberg–Marquardt method for the system of nonlinear equations, in which not only an L-M step and a corrected step are computed at every iteration but also a nonmonotone line search to find a new iteration point will be performed if a trial step is not accepted. To ensure the global convergence of the new method, a new nonmonotone line search technique is introduced for the merit function. The cubic convergence of the new method is proved under the local error bound condition which is weaker than nonsingularity. Some numerical results are reported, which shows that the algorithm is quite effective.