Volume: 40

In this paper, we study a class of derivative-free nonmonotone line search methods for solving nonlinear systems of equations, which includes the method N-DF-SANE proposed in Cheng and Li (IMA J Numer Anal 29:814–825, 2009). These methods correspond to derivative-free optimization methods applied to the minimization of a suitable merit function. Assuming that the mapping defining the system of nonlinear equations has Lipschitz continuous Jacobian, we show that the methods in the referred class need at most function evaluations to generate an -approximate stationary point to the merit function. For the case in which the mapping is strongly monotone, we present two methods with evaluation-complexity of .