A nonmonotone hybrid method for nonlinear systems
A nonmonotone hybrid method for solving nonlinear 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 rested on a number of problems and compared with well assessed methods for nonlinear systems. The results suggest that the potential of the proposed approach is sometimes considerable.
hybrid methods nonlinear systems nonmonotone line-search global convergence