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

2020/06/02 by de Oliveira, Fabiana R., Oliveira, Fabrícia R.
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2006.01559

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.

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• Damped Newton's Method on Riemannian Manifolds
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• Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
• On the superlinear convergence of Newton's method on Riemannian manifolds