Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound

Abstract

In this article, we analyze the convergence rate of the modified Levenberg-Marquardt (MLM) method under the Hölderian local error bound condition and the Hölderian continuity of the Jacobian, which are more general than the local error bound condition and the Lipschitz continuity of the Jacobian. Under special circumstances, the convergence rate of the MLM method coincides with the results presented by Fan. A globally convergent MLM algorithm by the trust region technique will also be given.

Keywords

• nonlinear equation
• levenberg-marquardt method
• convergence rate
• hölderian local error bound
• 65k05
• 90c30