A Cubic Regularized Newton's Method over Riemannian Manifolds
Optimization and Control
2018-05-16 v1
Abstract
In this paper we present a cubic regularized Newton's method to minimize a smooth function over a Riemannian manifold. The proposed algorithm is shown to reach a second-order -stationary point within iterations, under the condition that the pullbacks are locally Lipschitz continuous, a condition that is shown to be satisfied if the manifold is compact. Furthermore, we present a local superlinear convergence result under some additional conditions.
Cite
@article{arxiv.1805.05565,
title = {A Cubic Regularized Newton's Method over Riemannian Manifolds},
author = {Junyu Zhang and Shuzhong Zhang},
journal= {arXiv preprint arXiv:1805.05565},
year = {2018}
}