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Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds
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Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds
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Journal Article
Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds
2020
Overview
We extend some results of nonsmooth analysis from the Euclidean context to the Riemannian setting. Particularly, we discuss the concepts and some properties, such as the Clarke generalized covariant derivative, upper semicontinuity, and Rademacher theorem, of locally Lipschitz continuous vector fields on Riemannian settings. In addition, we present a version of the Newton method for finding a singularity of a special class of locally Lipschitz continuous vector fields. For mild conditions, we establish the well-definedness and local convergence of the sequence generated using the method in a neighborhood of a singularity.
Publisher
Springer Nature B.V
