题 目：Bilevel Optimization: Reformulations, Theory, and Algorithms
报告人：李庆娜 教授
单 位：北京理工大学
时 间：11月6日 8:00
地 点：龙子湖校区九章学堂南楼C座209
摘 要：Bilevel optimization is challenging because lower-level optimality is typically implicit and may be set-valued. This talk presents two complementary single-level reformulations. The first uses lower-level KKT conditions and leads to MPECs, where constraint qualifications and relaxation methods play a central role. Their application to bilevel hyperparameter optimization for support vector classification is also discussed. The second uses a lower-level gradient residual to construct an exact-penalty reformulation. Under suitable error-bound and Lipschitz assumptions, exactness can be established for sufficiently large penalty parameters. The resulting nonsmooth problem is solved by a prox-linear method, with a box-constrained quadratic dual and a spectral projected gradient solver in the simple bilevel case. Numerical results illustrate the effectiveness of the approach.
简 介：李庆娜，北京理工大学*51吃瓜-吃瓜网站
教授,博士生导师。湖南大学本科、博士，中科院51吃瓜
与系统科学研究院博士后.曾访问英国南安普顿大学、曼彻斯特大学，新加坡国立大学、香港中文大学等。主持多项国家自然科学基金青年、面上项目等. 任中国运筹学会51吃瓜
优化分会理事、算法与软件应用分会理事、北京运筹学会理事。《Pacific Journal of Optimization》特刊客座编委。主要研究最优化理论与算法及应用。著有专著《多维标度方法》,《Modern Optimization Methods》，及《凸分析讲义》等系列教材。获2020、2021北京市高校优秀毕业设计指导教师荣誉称号。获北京运筹学会优秀青年论文奖（2021），获批国家一流本科课程《最优化方法》(2025).
