Speaker
户将 Hu Jiang
Assistant Professor of YMSC
Time
Tues. & Wed., 15:20-16:55,
Sept. 16-Dec. 3, 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.
Prerequisite：
Calculus, Linear Algebra, Numerical Optimization
Reference：
1. P-A. Absil, Robert Mahony, and Rodolphe Sepulchre. Optimization algorithms on matrix manifolds. Princeton University Press, 2008.
2. Nicolas Boumal. An introduction to optimization on smooth manifolds. Cambridge University Press, 2023.
3. Jiang Hu, Xin Liu, Zai-Wen Wen, and Ya-Xiang Yuan. A brief introduction to manifold optimization. Journal of the Operations Research Society of China 8, no. 2 (2020): 199-248.
4. Papers by the instructor about this topic
Target Audience:
Undergraduate students, Graduate students
Teaching Language: Depends on audience
