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Optimization flows landing on the Stiefel manifold
高斌
（中国科学院数学与系统科学研究院）
报告时间：2025年11月4日 星期二 上午10：30-11：30
报告地点：沙河校区E806
报告摘要：We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization flow follows a path that is not always on the manifold but asymptotically lands on the manifold. We introduce a generalized Stiefel manifold to which we extend the canonical metric of the Stiefel manifold. We show that the vector field of the proposed flow can be interpreted as the sum of a Riemannian gradient on a generalized Stiefel manifold and a normal vector. Moreover, we prove that the proposed flow globally converges to the set of critical points, and any local minimum and isolated critical point is asymptotically stable.
报告人简介：高斌，中国科学院数学与系统科学研究院计算数学所副研究员。2019年毕业于中国科学院数学与系统科学研究院。曾先后赴比利时、德国从事博士后研究。其主要研究兴趣是矩阵和张量流形上的优化算法。曾获中国科学院院长特别奖、钟家庆数学奖。受到中国科协青托工程、中科院和国家海外高层次人才计划等项目资助。
邀请人： 谢家新
