On the global convergence of a parameter-adjusting Levenberg-Marquardt method

Abstract

The Levenberg-Marquardt (LM) method is a classical but popular method for solving nonlinear equations. Based on the trust region technique, we propose a parameter-adjusting LM (PALM) method, in which the LM parameter $\mu_k$ is self-adjusted at each iteration based on the ratio between actual reduction and predicted reduction. Under the level-bounded condition, we prove the global convergence of PALM. We also propose a modified parameter-adjusting LM (MPALM) method. Numerical results show that the two methods are very efficient.