# Riemannian Interior Point Methods for Constrained Optimization on Manifolds

arXiv: https://arxiv.org/abs/2203.09762 · HTML: https://mlsanity.com/paper/2203.09762/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2022.

## Built on by (most cited first, 3 of 3)

- [Iso-Riemannian Optimization on Learned Data Manifolds](https://mlsanity.com/paper/2510.21033/) (2025)
- [Riemannian Zeroth-Order Gradient Estimation with Structure-Preserving Metrics for Geodesically Incomplete Manifolds](https://mlsanity.com/paper/2601.08039/) (2026)
- [Optimization over the intersection of manifolds](https://mlsanity.com/paper/2605.22736/) (2026)

## Abstract (arXiv)

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish its local superlinear and quadratic convergence under the standard assumptions. Moreover, we show its global convergence when it is combined with a classical line search. Our method is a generalization of the classical framework of primal-dual interior point methods for nonlinear nonconvex programming. Numerical experiments show the stability and efficiency of our method.