A nonmonotone hybrid method for nonlinear systems

A nonmonotone hybrid method for solving nonhnear systems is proposed. The idea consists in matching a Newton-like method stabilized by nonmonotone line-search with a cheap direct search method that reduces monotonically the merit function. The aim is to enlarge the convergence domain of the Newton-like method without either losing its local convergence rate or introducing too much additional computational work. The proposed method has been extensively tested on a number of problems and compared with well assessed methods for nonhnear systems. The results suggest that the potential of the proposed approach is sometimes considerable