Introduction to Manifold Optimization

Speaker：

Jiang Hu 户将（YMSC）

Time：

Tues. & Wed., 15:20-16:55, Sept. 16-Dec. 3, 2025; Wed., 13:30-15:05, Nov. 5, 12, 19, 2025

Venue：

C654, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 276 366 7254

Passcode: YMSC

Description:

Manifold optimization is a modern mathematical framework that unifies differential geometry and optimization for problems with variables constrained to smooth non-Euclidean spaces. This course introduces its core concepts, algorithms, theories, and representative applications in computational science, statistics, machine learning, and artificial intelligence.

The course begins with a survey of representative applications of manifold optimization in scientific computing and artificial intelligence. It then introduces the extension of classical Euclidean optimization methods to non-Euclidean manifolds, highlighting the geometric structures and central ideas underlying the design of manifold optimization algorithms. Topics include gradient methods, Newton’s method, and trust-region methods, as well as Riemannian stochastic optimization algorithms for large-scale problems. Subsequently, the course presents manifold optimization methods in distributed and federated learning settings, covering algorithmic designs and theoretical analyses. The course will also integrate representative application cases and coding practices to deepen students’ understanding of different algorithms and their practical relevance.