报告题目 (Title)：Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization（数据驱动的Wasserstein分布鲁棒优化的矩松弛方法）
报告人 (Speaker)：钟粟晗 副教授（上海交通大学）
报告时间 (Time)：2025年12月16日(周二) 16：00
报告地点 (Place)：GJ303
邀请人(Inviter)：周安娃
报告摘要：We propose moment relaxations for data-driven p-Wasserstein distributionally robust optimization (p-WDRO) problems that are defined by polynomials. We identify conditions dependent on p and defining polynomial degrees such that the proposed k-th order moment relaxations preserve the asymptotic consistency (i.e., the relaxation gap decreases linearly with respect to the Wasserstein radius) of the original p-WDRO. In particular, these conditions translate to effective bounds on k, which lead to polynomially sized semidefinite optimization formulations that are compatible with existing solvers. Numerical experiments on a two-stage production problem are included to show that the our conditions can hold for the lowest relaxation order k=1 (Shor relaxation) in some practical cases.