报告承办单位: 数学与统计学院

报告题目: Exact-Penalty Prox-Linear Methods for Bilevel Optimization with ℓ1 Lower-Level Gradient Penalty

报告人姓名: 李庆娜

报告人所在单位: 北京理工大学

报告人职称: 教授、博士生导师

报告时间: 2026年6月28日 星期日 下午16:30

报告地点: 理科楼A212

邀请人：李姣

报告摘要: Bilevel optimization is a fundamental framework for hierarchical decision-making, but its solution is challenging due to the implicit and typically set-valued nature of the lower-level optimality condition. In this paper, we study bilevel optimization problems through an exact-penalty reformulation based on the ℓ1-norm of the lower-level gradient. Under suit able regularity assumptions, we show that this penalty defines a distance-bound function and yields an exact penalty property for sufficiently large penalty parameters. To solve the resulting nonsmooth penalized problem, we propose an exact-penalty prox-linear (EPPL) method and establish a stationarity-oriented convergence guarantee. We further specialize 1 2 3 4 5 6 7 8 9 the method to the simple bilevel setting, where the subproblem admits an explicit dual re- 10 formulation as a box-constrained quadratic program. This structure leads to a dual spectral 11 projected gradient method with closed-form primal recovery, for which convergence of the 12 inner dual iterates is proved. Numerical experiments on a minimum-norm least-squares 13 bilevel model show that the proposed method is effective in reducing both the lower-level 14 and upper-level gaps to high accuracy. Compared with several existing methods, the 15 proposed approach attains the best final solution accuracy on the tested instance. This is a joint work with Yutong Zheng and Jiani Li.

报告人简介：李庆娜，北京理工大学数学与统计学院教授,博士生导师。湖南大学本科、博士，中科院数学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. 任中国运筹学会数学优化分会理事、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).