讲座主题：Optimality conditions and numerical algorithms for a class of Minimax Bilevel Optimization Problems

专家姓名：童小娇

工作单位：湘潭大学

讲座时间：2026年07月27日 16:00-17:00

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

This talk focuses on a class of minmax bilevel optimization problems, which comes from many applications such as Stackelberg games, machine learning, and power systems. We introduce optimality conditions and develop efficient first-order algorithms for this class of problems in this research. Firstly, we establish the optimality conditions for minimax bilevel problems by reconstructing the lower-level problem through its Karush-Kuhn-Tucker (KKT) conditions and value function. Secondly, we develop a penalty method framework to approximately solve the minimax bilevel problem by transforming it into a single-level minimax problem. Thirdly, we design a projected gradient multi-step ascent descent method to solve the resulting minimax problem, which can find an ℇ-KKT solution for the original minimax bilevel problem within O(ϵ−3log ( ϵ−1)) iterations. To improve the convergence rate of the algorithm, we provide its Nesterov accelerated extension with O(ϵ−3log (ϵ−1)) iteration complexity. Finally, we demonstrate the effectiveness of our model and algorithms through numerical experiments on various minimax bilevel optimization problems and a economic dispatch in the power system.

主讲人介绍：

童小娇，湘潭大学/湖南第一师范学院 二级教授，国务院政府特殊津贴专家，湘潭大学博士生导师。曾任湖南第一师范学院校长，中国运筹学会第十一届副理事长、中国工业与应用数学学会第六、七届常务理事，湖南省运筹学会第一、二届理事长。

研究方向为最优化理论与方法、电力系统中的数学优化方法等，在半光滑牛顿法、随机优化算法和风险管理、电力系统经济调度的数学方法等开展了系列理论与应用研究。获湖南省自然科学二等奖2项、湖南省教学成果一等奖1项。主持国家自然科学基金重点项目1项、面上项目和天元专项10项，出版电力优化相关学术专著获“国家科学技术学术著作出版基金”资助，在最优化和电力系统分析相关高影响期刊发表学术论文100余篇。