报告人：林贵华教授

报告题目：A novel approach for bilevel programs based on Wolfe duality

摘要：In this talk, we focus on a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be reformulated as a mathematical program with equilibrium constraints (MPEC for short). However, since the MPEC does not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. In this paper, we apply the Wolfe duality to show that, under very mild conditions, the bilevel program is equivalent to a new single-level reformulation (WDP for short) in the globally and locally optimal sense. We give an example to show that, unlike the MPEC reformulation, WDP may satisfy the Mangasarian-Fromovitz constraint qualification at its feasible points. We give some properties of the WDP reformulation and the relations between the WDP and MPEC reformulations. We further propose a relaxation method for solving WDP and investigate its limiting behavior. Comprehensive numerical experiments indicate that, although solving WDP directly does not perform very well in our tests, the relaxation method based on the WDP reformulation is quite efficient.

报告时间：2022年5月31号上午9:00-11:30

报告形式：腾讯会议；会议号：755 393 756

报告人简介：林贵华教授于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人怀学者、管理科学与工程系主任。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、European Journal of Operational Research等国际知名期刊上发表学术论文80余篇。主持国家自科面上项目4项、自科重点项目子课题2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、中国双法研究会经济数学与管理数学分会常务理事等，《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。