Academic Report of School of Mathematical Sciences [2025] No. 139

(Series Report for High-Level University Construction No. 1241)

Title：Theoretical and numerical comparison of nine single-level reformulations for bilevel programs

Speaker：Professor Guihua Lin(Shanghai University)

Time：10:30-11:30，December 8, 2025

Location: Conference Room 305, Alumni Square, Shenzhen University

Abstract: 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.

Speaker Profile：Lin Guihua earned his Ph.D. from Kyoto University, Japan in 2004. He is a Wei Chang Distinguished Professor at Shanghai University and leads a key innovation team at Shanghai's high-level local universities. He has been selected for the Shanghai Leading Talent Program and the Liaoning Province Hundred-Thousand-Ten Thousand Talent Project. His research interests focus on various optimization problems related to equilibrium and their applications in management science. He has published over 100 academic papers in internationally renowned journals such as the INFORMS Journal on Computing, Mathematical Programming, SIAM Journal on Optimization, Mathematics of Computation, and Automatica. He has led five National Natural Science Foundation of China projects, two sub-projects under key national natural science initiatives, and seven provincial/ministerial-level projects. Currently serving as Vice President of the Economic Mathematics and Management Mathematics Branch of the Chinese Society of Mathematical Methods in Science and Engineering, Senior Council Member of the Mathematical Programming Branch of the Chinese Operations Research Society, and Council Member of the Shanghai Operations Research Society. He is also an editorial board member for the Pacific Journal of Optimization and Operations Research and Management. Two of his doctoral students have been selected for the National “Four Young Talents” Program, and three others have received provincial/ministerial-level talent honors.

Faculty and students are welcome to attend!

Invited by: Hu Yaohua

School of Mathematical Sciences

December 2, 2025