数学与统计学院学术报告[2023] 028号

(高水平大学建设系列报告799号)

报告题目: Solving Bilevel Programs Based on Lower-level Duality

报告人：林贵华教授 (上海大学)

报告时间：2023年4月27日10：30 - 11：30

报告地点：汇星楼金融科技学院教室一号报告厅

报告内容：In this talk, we focus on bilevel programs, which have many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform bilevel programs into single-level optimization problems. The most popular approach is to replace the lower-level programs by their KKT conditions and then bilevel programs can be reformulated as mathematical programs with equilibrium constraints (MPEC). However, since MPECs do not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. Recently, we apply the lower-level Wolfe duality and the lower-level Mond-Weir duality to present two new single-level reformulations for bilevel programs. We show through examples that, unlike the MPEC reformulation, the new reformulations may satisfy the Mangasarian-Fromovitz constraint qualification at their feasible points. We investigate their properties and the relations with the MPEC reformulation. We further propose some relaxation methods and numerical experiments indicate that, although solving the new reformulations directly does not perform very well in our tests, the relaxation methods are more efficient than the MPEC approach.

报告人简历：

林贵华于2004年博士毕业于日本京都大学，曾任京都大学JSPS外国人特别研究员，现任上海大学管理学院教授、人怀学者。研究兴趣主要是与均衡相关的各种最优化问题及其在管理科学中的应用，在SIAM Journal on Optimization、Mathematical Programming、Mathematics of Computation等国际知名期刊上发表学术论文80余篇。主持国家自然科学基金项目4项、省部级项目5项。现任中国运筹学会理事、中国运筹学会数学规划分会理事、上海运筹学会理事等，《Pacific Journal of Optimization》、《运筹与管理》编委。2007年入选辽宁省百千万人才工程，所指导博士生曾获2014年度辽宁省优秀博士学位论文。

欢迎师生参加！

                                               　数学与统计学院

                                                2023年4月26日