An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations

Abstract

A modified Levenberg–Marquardt method for solving singular systems of nonlinear equations was proposed by Fan [J Comput Appl Math. 2003;21;625–636]. Using trust region techniques, the global and quadratic convergence of the method were proved. In this paper, to improve this method, we decide to introduce a new Levenberg–Marquardt parameter while also incorporate a new nonmonotone technique to this method. The global and quadratic convergence of the new method is proved under the local error bound condition. Numerical results show the new algorithm is efficient and promising.

Keywords:

• Levenberg–Marquardt method
• singular nonlinear equations
• local error bound condition
• nonmonotone technique
• global and quadratic convergence

Notes

No potential conflict of interest was reported by the authors.