A Global Version of the Newton Method for Finding a Singularity of the Nonsmooth Vector Fields on Riemannian Manifolds

Abstract

This paper is concerned with an algorithm for finding a singularity of the nonsmooth vector fields. Firstly, we discuss the main results of the Newton method presented in [1] for solving the aforementioned problem. Combining this method with a nonmonotone line search strategy, we then propose a global version of the Newton Method. Finally, numerical experiments illustrating the practical advantages of the proposed scheme are reported.