A Global Newton Method for the Nonsmooth Vector Fields on Riemannian Manifolds

Fabiana R. Oliveira () and Fabrícia R. Oliveira ()
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Fabiana R. Oliveira: Universidade Federal de Goiás
Fabrícia R. Oliveira: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 1, No 11, 259-273

Abstract: Abstract This paper proposes and analyzes a globalized version of the Newton method for finding a singularity of the nonsmooth vector fields. Basically, the new method combines a version of nonsmooth Newton method with a nonmonotone line search strategy. The global convergence analysis of the proposed method as well as results on its rate are established under mild assumptions. Finally, numerical experiments illustrating the practical advantages of the proposed scheme are reported.

Keywords: Riemannian manifold; Locally Lipschitz continuous vector fields; Global convergence; Regularity; Nonmonotone line search; 49J52; 58C05; 58C15; 90C56 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01881-4

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