Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds

Fabiana R. de Oliveira () and Orizon P. Ferreira ()
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Fabiana R. de Oliveira: IME, Universidade Federal de Goiás
Orizon P. Ferreira: IME, Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 11, 522-539

Abstract: Abstract 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.

Keywords: Riemannian manifold; Locally Lipschitz continuous vector fields; Clarke generalized covariant derivative; Semismooth vector field; Regularity; Newton method; 90C30; 49J52; 90C56 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01656-3

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