数学科学学院学术报告[2025] 139号

(高水平大学建设系列报告1241号)

报告题目：Theoretical and numerical comparison of nine single-level reformulations for bilevel programs

报告人：林贵华 教授 (上海大学)

报告时间：2025年12月8日上午10:30-11:30

报告地点：深圳大学校友广场305会议室

内容摘要：This talk discusses a bilevel program. To solve this bilevel program, it is generally necessary to transform it into some single-level optimization problem. One approach is to replace the lower-level program by its KKT conditions to transform the bilevel program as a mathematical program with complementarity constraints (MPCC). Another approach is to apply the lower-level Wolfe/Mond-Weir/extended Mond-Weir duality to transform the bilevel program into some duality-based single-level reformulations, called WDP, MDP, and eMDP respectively in the literature. In this paper, inspired by a conjecture from a recent publication that the tighter feasible region of a reformulation, the better its numerical performance, we present five new duality-based single-level reformulations, called TWDP/TMDP/eTMDP/ETMDP/eETMDP, with tighter feasible regions. Our main goal is to compare all above-mentioned reformulations by designing some direct and relaxation algorithms with projection and implementing these algorithms on 450 test examples generated randomly. Our numerical experiments show that, whether overall comparison or pairwise comparison, at least in our tests, in terms of dominant cases and objective values, WDP/MDP/TWDP/TMDP/ETMDP were always better than MPCC, while eMDP/eTMDP/eETMDP were always the worst ones among eight duality-based reformulations, which indicates that the above conjecture is incorrect. In particular, for the relaxation algorithms, WDP/MDP/TWDP/TMDP performed 4-5 times better than MPCC, while eMDP/eTMDP/ETMDP/eETMDP performed at least 1.8 times better than MPCC in terms of dominant cases.

报告人简历：林贵华于2004年博士毕业于日本京都大学，上海大学伟长学者特聘教授，上海高水平地方高校重点创新团队负责人，入选上海领军人才计划、辽宁省百千万人才工程等。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INFORMS Journal on Computing、Mathematical Programming、SIAM Journal on Optimization、Mathematics of Computation、Automatica等国际知名期刊发表学术论文100余篇。主持国家自然科学基金项目5项、国家自然科学重点项目子课题2项、省部级项目7项。现任中国双法会经济数学与管理数学分会副理事长、中国运筹学会数学规划分会资深理事、上海运筹学会理事等，《Pacific Journal of Optimization》、《运筹与管理》编委。所指导研究生获得国家四青人才2人、省部级人才3人。

欢迎师生参加！

邀请人：胡耀华

数学科学学院

2025年12月2日