A NONMONOTONE LEVENBERG-MARQUARDT METHOD WITH CORRECTION FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

It is well known that Levenberg-Marquardt (LM) method is widely used for solving nonlinear equations. In this paper, we give an extension of LM method and propose a nonmonotone LM method with correction which produces the LM parameter according to the new nonmonotone strategy of Grippo, Lampariello and Lucidi. Moreover, not only an LM step but also a correction step are computed at every iteration in our proposed nonmonotone LM method with correction. The cubic convergence of the proposed method is proved under the local error bound condition which is weaker than nonsingularity. Some numerical results confirm the feasibility and effectiveness of the proposed algorithm.