Convergence properties of a family of inexact Levenberg-Marquardt methods

Abstract

We present a family of inexact Levenberg-Marquardt (LM) methods for the nonlinear equations which takes more general LM parameters and perturbation vectors. We derive an explicit formula of the convergence order of these inexact LM methods under the H$ \mathrm{\ddot{o}} $derian local error bound condition and the H$ \mathrm{\ddot{o}} $derian continuity of the Jacobian. Moreover, we develop a family of inexact LM methods with a nonmonotone line search and prove that it is globally convergent. Numerical results for solving the linear complementarity problem are reported.

Keywords

• nonlinear equations
• inexact levenberg-marquardt method
• global convergence
• convergence rate
• h$ \mathrm{\ddot{o}} $derian local error bound