Speaker: 黄文教授，厦门大学

Inviter: 丁超研究员

Title: Riemannian Optimization and a Riemannian Proximal Newton-CG Method

Language: English

Time & Venue: 2025.11.12 14:00-15:30 数学院思源楼615

Abstract: Optimization on Riemannian manifolds, also called Riemannian optimization, considers finding an optimum of a real-valued function defined on a Riemannian manifold. Riemannian optimization has been a topic of much interest over the past few years due to many important applications. In this presentation, the framework of Riemannian optimization is introduced, and the current state of Riemannian optimization algorithms are briefly reviewed. To show a research focus and difficulties of Riemannian optimization, we generalize the proximal Newton method to the Riemannian setting. A globalization technique using the truncated conjugate gradient method has also been developed. It is proven that the proposed Riemannian proximal Newton-CG method converges globally and superlinearly locally. The difficulties therein are highlighted. Numerical experiments verify the theoretical results. Moreover, it is empirically shown that the proposed method outperforms the state-of-the-art methods using sparse PCA and compressed modes problems.