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Mathematics > Optimization and Control

arXiv:1803.05126 (math)
[Submitted on 14 Mar 2018 (v1), last revised 19 Jul 2018 (this version, v2)]

Title:Damped Newton's Method on Riemannian Manifolds

Authors:M. A. A. Bortoloti, T. A. Fernandes, O. P. Ferreira, Jinyun Yuan
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Abstract:A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the Riemannian version of the classical Newton's method after a finite number of iterations, consequently its convergence rate is superlinear/quadratic. Moreover, numerical experiments illustrate that the damped Newton's method has better performance than Newton's method in number of iteration and computational time.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1803.05126 [math.OC]
  (or arXiv:1803.05126v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1803.05126

Submission history

From: Teles Fernandes [view email]
[v1] Wed, 14 Mar 2018 03:54:39 UTC (40 KB)
[v2] Thu, 19 Jul 2018 14:26:41 UTC (40 KB)
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