应用数学青年讨论班(午餐会)--Capacity-Constrained Optimal Transport: Models and Algorithms
报告人：吴天昊(清华大学)
时间：2025-04-23 11:45-13:00
地点：智华楼四元厅
摘要:
In this talk, we explore algorithms for a variant of optimal transport called capacity-constrained optimal transport, which adds extra constraints on the set of feasible couplings to limit the mass transported between each pair of source and sink. Due to the large number of constraints in this problem, existing algorithms are both time-consuming and space-consuming. We consider a regularized problem that naturally satisfies the capacity constraints and consequently propose an alternating algorithm called the double regularization method. In our method, each alternate iteration step is to solve several single-variable equations. Theoretical analysis further provides a convergence guarantee to our method. Building on this, we introduce the sampled double regularization method based on importance sampling. In this approach, we approximate each single-variable equation by sampling a subset of its terms according to a designed sampling distribution. Theoretical analysis establishes the unbiasedness of this estimator and provides a bound on the approximation error.
报告人信息：
吴天昊，清华大学数学科学系博士生，主要研究方向为最优输运及其应用，特别是在图问题与图算法中的应用。
欢迎大家参与4月23号的午餐会。报告时间是12:00-13:00，午餐于11:45开始提供。请有意参与的老师和同学在4月22日15:00前填写以下问卷 https://www.wjx.cn/vm/mBjQe3I.aspx# .
