A Shamanskii-like self-adaptive Levenberg-Marquardt method for nonlinear equations

In this paper, we are concerned with the Shamanskii-like self-adaptive Levenberg-Marquardt methods for nonlinear equations. We consider two choices of Levenberg-Marquardt parameter. One of them is the standard self-adaptive Levenberg-Marquardt parameter, the other is nonmonotone self-adaptive Levenberg-Marquardt parameter by using the nonmonotone technique of Grippo, Lampariello and Lucidi. Under the error bound condition which is weaker than nonsingularity, we show that the Shamanskii-like self-adaptive Levenberg-Marquardt methods converge with Q-order (m + 1). Numerical experiments show the new algorithms are efficient and promising. (C) 2018 Elsevier Ltd. All rights reserved.