On the convergence rate of the inexact Levenberg-Marquardt method

In this paper we study the convergence rate of the inexact Levenberg-Marquardt method for nonlinear equations. Under the local error bound condition which is weaker than nonsingularity, we derive an explicit formula of the convergence order of the inexact LM method, which is a continuous function with respect to not only the LM parameter but also the perturbation vector. The new formula includes many convergence rate results in the literature as its special cases.