Riemannian Interior Point Methods for Constrained Optimization on Manifolds

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 stan...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Lai, Zhijian, Yoshise, Akiko
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Nonlinear programming
Optimization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.09762