English

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 ϵ\epsilon-stationary point within O(1/ϵ32)\mathcal{O}(1/\epsilon^{\frac{3}{2}}) 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.

Keywords

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}
}
R2 v1 2026-06-23T01:55:14.066Z