数学科学学院学术报告
Riemannian Optimization and a Riemannian Proximal Newton-CG Method
黄文
（厦门大学数学科学学院）
报告时间：2025年11月11日 星期二 上午9：30-10:30
报告地点：沙河校区E806
报告摘要：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.
报告人简介：黄文教授，2014年毕业于佛罗里达州立大学，获得应用与计算数学博士学位。2014年至2016年在比利时新鲁汶大学数学工程系担任博士后。2016年至2018年在美国莱斯大学计算与应用数学系担任法伊佛博士后讲师。于2018年9月加入厦门大学。他的主要研究兴趣在黎曼流形上的优化算法及其应用，包括信号处理，图像处理，计算机视觉，网络成分分析，统计，机器学习等大规模问题的理论以及算法实现。研究成果发表在SIOPT，SISC，MATH PROGRAM，NUMER MATH等主流期刊。他开发了用来解决流形优化问题的C++软件工具包ROPTLIB。主持国家自然科学基金青年及面上项目，并于2021年入选国家级高层次人才青年项目。
邀请人：谢家新
