数学科学学院学术报告
On Second-Order Optimization Methods
叶荫宇
（斯坦福大学）
报告时间：2026年7月24日 星期五 下午15：00-16：00
报告地点：沙河校区E806
报告摘要：The second-order optimization methods have mathematical advantages over the zeroth or first-order methods for high precision and super-linear convergence. However, the obstacles for applying the second-order methods are 1) The second-order derivative Hessian is hard to acquire, 2) even we have, it is computationally expensive to utilize it. We address these two issues for a convex optimization problem on computing market equilibria such as the Fisher market. We first show that the second-order Hessian information is no harder than the first-order to possess. Then, to address the expensive computation step in second-order methods, we introduce explicitly approximation Newton steps with high-probability fast-convergence guarantees and a scaling matrix that optimally minimizes Newton-system’s condition number. Preliminary tests are presented to justify the capability of the proposed methods for solving large-scale market equilibrium problems.
报告人简介：叶荫宇教授是斯坦福大学管理科学与工程系及计算数学工程研究院李国鼎讲席教授，目前还担任香港中文大学（深圳）数据科学学院特聘教授、上海交通大学智能计算研究院特聘教授。他的研究重点是连续和离散优化、数据科学应用、数值算法设计、博弈论与市场均衡以及运筹学。作为内点法、圆锥线性规划和强化学习算法等领域的先驱，他曾荣获多项重要奖项，包括2009年约翰·冯·诺依曼理论奖、国际数学规划2012 Tseng Lectureship Prize以及2014年美国应用数学学会优化奖。他的研究成果在谷歌学术搜索中已被引用超过65,000次。
邀请人：韩德仁、谢家新
