On the superlinear convergence of Newton's method on Riemannian manifolds

2016/11/13 by Fernandes, Teles A., Ferreira, Orizon P., Yun, Yuan J. · 2 citations
#49M15 and 65K05 #90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1611.04207

Abstract

In this paper we study the Newton's method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of covariant derivative of the vector field at its singularity, we establish the well definition of the method in a suitable neighborhood of this singularity. Moreover, we also show that the generated sequence by Newton method converges for the solution with superlinear rate.

Cited by

• Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems
• Local near-quadratic convergence of Riemannian interior point methods

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