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三元名家论坛系列报告之第984期:Optimality conditions and numerical algorithms for a class of Minimax Bilevel Optimization Problems
- 来源：
- 学校官网
- 收录时间：
- 2026-07-24 03:01:26
- 时间：
- 2026-07-27 16:00:00
- 地点：
- 数学院大会议室341
- 报告人：
- 童小娇
- 学校：
- 烟台大学
- 关键词：
- minimax bilevel optimization, optimality conditions, first-order algorithms, KKT conditions, value function, penalty method, projected gradient method, Nesterov acceleration
- 简介：
- 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.
- -/- 3
报告介绍：
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.
报告人介绍：
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。
报告图片：
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